Elements of the Representation Theory of the Jacobi Group:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Springer Basel
1998
|
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms. ----------------- The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. (Zentralblatt MATH) This book is certainly recommended for researchers interested in modular and automorphic forms. (Mathematical Reviews) This book complements the book on Jacobi forms by M. Eichler and D. Zagier and includes many of the author's original results. It can be read, however, independently of other sources, and it will be very useful for researchers interested in algebraic groups and number theory. (Mathematica) |
| Beschreibung: | 1 Online-Ressource (XIII, 213p) |
| ISBN: | 9783034802833 9783034802826 |
| DOI: | 10.1007/978-3-0348-0283-3 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042421844 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1998 |||| o||u| ||||||eng d | ||
| 020 | |a 9783034802833 |c Online |9 978-3-0348-0283-3 | ||
| 020 | |a 9783034802826 |c Print |9 978-3-0348-0282-6 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0283-3 |2 doi | |
| 035 | |a (OCoLC)863858450 | ||
| 035 | |a (DE-599)BVBBV042421844 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 516.35 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Berndt, Rolf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elements of the Representation Theory of the Jacobi Group |c by Rolf Berndt, Ralf Schmidt |
| 264 | 1 | |a Basel |b Springer Basel |c 1998 | |
| 300 | |a 1 Online-Ressource (XIII, 213p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Modern Birkhäuser Classics | |
| 500 | |a The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms. ----------------- The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. (Zentralblatt MATH) This book is certainly recommended for researchers interested in modular and automorphic forms. (Mathematical Reviews) This book complements the book on Jacobi forms by M. Eichler and D. Zagier and includes many of the author's original results. It can be read, however, independently of other sources, and it will be very useful for researchers interested in algebraic groups and number theory. (Mathematica) | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Group Theory and Generalizations | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Darstellungstheorie |0 (DE-588)4148816-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Jacobi-Gruppe |0 (DE-588)4417643-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Darstellungstheorie |0 (DE-588)4148816-7 |D s |
| 689 | 0 | 1 | |a Jacobi-Gruppe |0 (DE-588)4417643-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Schmidt, Ralf |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-0348-0283-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027857261 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153095376076800 |
|---|---|
| any_adam_object | |
| author | Berndt, Rolf |
| author_facet | Berndt, Rolf |
| author_role | aut |
| author_sort | Berndt, Rolf |
| author_variant | r b rb |
| building | Verbundindex |
| bvnumber | BV042421844 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863858450 (DE-599)BVBBV042421844 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0283-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03572nmm a2200541zc 4500</leader><controlfield tag="001">BV042421844</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1998 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034802833</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-0348-0283-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783034802826</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-0348-0282-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-0348-0283-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863858450</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421844</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.35</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Berndt, Rolf</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Elements of the Representation Theory of the Jacobi Group</subfield><subfield code="c">by Rolf Berndt, Ralf Schmidt</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel</subfield><subfield code="b">Springer Basel</subfield><subfield code="c">1998</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XIII, 213p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Modern Birkhäuser Classics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms. ----------------- The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. (Zentralblatt MATH) This book is certainly recommended for researchers interested in modular and automorphic forms. (Mathematical Reviews) This book complements the book on Jacobi forms by M. Eichler and D. Zagier and includes many of the author's original results. It can be read, however, independently of other sources, and it will be very useful for researchers interested in algebraic groups and number theory. (Mathematica)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, algebraic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebraic Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group Theory and Generalizations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Darstellungstheorie</subfield><subfield code="0">(DE-588)4148816-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Jacobi-Gruppe</subfield><subfield code="0">(DE-588)4417643-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Darstellungstheorie</subfield><subfield code="0">(DE-588)4148816-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Jacobi-Gruppe</subfield><subfield code="0">(DE-588)4417643-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schmidt, Ralf</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-0348-0283-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027857261</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042421844 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9783034802833 9783034802826 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857261 |
| oclc_num | 863858450 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIII, 213p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer Basel |
| record_format | marc |
| series2 | Modern Birkhäuser Classics |
| spelling | Berndt, Rolf Verfasser aut Elements of the Representation Theory of the Jacobi Group by Rolf Berndt, Ralf Schmidt Basel Springer Basel 1998 1 Online-Ressource (XIII, 213p) txt rdacontent c rdamedia cr rdacarrier Modern Birkhäuser Classics The Jacobi group is a semidirect product of a symplectic group with a Heisenberg group. It is an important example for a non-reductive group and sets the frame within which to treat theta functions as well as elliptic functions - in particular, the universal elliptic curve. This text gathers for the first time material from the representation theory of this group in both local (archimedean and non-archimedean) cases and in the global number field case. Via a bridge to Waldspurger's theory for the metaplectic group, complete classification theorems for irreducible representations are obtained. Further topics include differential operators, Whittaker models, Hecke operators, spherical representations and theta functions. The global theory is aimed at the correspondence between automorphic representations and Jacobi forms. This volume is thus a complement to the seminal book on Jacobi forms by M. Eichler and D. Zagier. Incorporating results of the authors' original research, this exposition is meant for researchers and graduate students interested in algebraic groups and number theory, in particular, modular and automorphic forms. ----------------- The book is very well written and gives an up to date collection of the results known. It will be quite useful for everyone working in the field. (Zentralblatt MATH) This book is certainly recommended for researchers interested in modular and automorphic forms. (Mathematical Reviews) This book complements the book on Jacobi forms by M. Eichler and D. Zagier and includes many of the author's original results. It can be read, however, independently of other sources, and it will be very useful for researchers interested in algebraic groups and number theory. (Mathematica) Mathematics Geometry, algebraic Group theory Number theory Algebraic Geometry Number Theory Group Theory and Generalizations Mathematik Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Jacobi-Gruppe (DE-588)4417643-0 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 s Jacobi-Gruppe (DE-588)4417643-0 s 1\p DE-604 Schmidt, Ralf Sonstige oth https://doi.org/10.1007/978-3-0348-0283-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berndt, Rolf Elements of the Representation Theory of the Jacobi Group Mathematics Geometry, algebraic Group theory Number theory Algebraic Geometry Number Theory Group Theory and Generalizations Mathematik Darstellungstheorie (DE-588)4148816-7 gnd Jacobi-Gruppe (DE-588)4417643-0 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4417643-0 |
| title | Elements of the Representation Theory of the Jacobi Group |
| title_auth | Elements of the Representation Theory of the Jacobi Group |
| title_exact_search | Elements of the Representation Theory of the Jacobi Group |
| title_full | Elements of the Representation Theory of the Jacobi Group by Rolf Berndt, Ralf Schmidt |
| title_fullStr | Elements of the Representation Theory of the Jacobi Group by Rolf Berndt, Ralf Schmidt |
| title_full_unstemmed | Elements of the Representation Theory of the Jacobi Group by Rolf Berndt, Ralf Schmidt |
| title_short | Elements of the Representation Theory of the Jacobi Group |
| title_sort | elements of the representation theory of the jacobi group |
| topic | Mathematics Geometry, algebraic Group theory Number theory Algebraic Geometry Number Theory Group Theory and Generalizations Mathematik Darstellungstheorie (DE-588)4148816-7 gnd Jacobi-Gruppe (DE-588)4417643-0 gnd |
| topic_facet | Mathematics Geometry, algebraic Group theory Number theory Algebraic Geometry Number Theory Group Theory and Generalizations Mathematik Darstellungstheorie Jacobi-Gruppe |
| url | https://doi.org/10.1007/978-3-0348-0283-3 |
| work_keys_str_mv | AT berndtrolf elementsoftherepresentationtheoryofthejacobigroup AT schmidtralf elementsoftherepresentationtheoryofthejacobigroup |