Elements of the Representation Theory of the Jacobi Group:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1998
|
| Schriftenreihe: | Progress in Mathematics
163 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | After Pyatetski-Shapiro [PSI] and Satake [Sal] introduced, independent of one another, an early form of the Jacobi Theory in 1969 (while not naming it as such), this theory was given a definite push by the book The Theory of Jacobi Forms by Eichler and Zagier in 1985. Now, there are some overview articles describing the developments in the theory of the Jacobi group and its automor phic forms, for instance by Skoruppa [Sk2], Berndt [Be5] and Kohnen [Ko]. We refer to these for more historical details and many more names of authors active in this theory, which stretches now from number theory and algebraic geometry to theoretical physics. But let us only briefly indicate several - sometimes very closely related - topics touched by Jacobi theory as we see it: • fields of meromorphic and rational functions on the universal elliptic curve resp. universal abelian variety • structure and projective embeddings of certain algebraic varieties and homogeneous spaces • correspondences between different kinds of modular forms • L-functions associated to different kinds of modular forms and autom- phic representations • induced representations • invariant differential operators • structure of Hecke algebras • determination of generalized Kac-Moody algebras and as a final goal related to the here first mentioned • mixed Shimura varieties and mixed motives |
| Beschreibung: | 1 Online-Ressource (XIII, 216 p) |
| ISBN: | 9783034887724 9783764359225 |
| ISSN: | 0743-1643 |
| DOI: | 10.1007/978-3-0348-8772-4 |
Internformat
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| 245 | 1 | 0 | |a Elements of the Representation Theory of the Jacobi Group |c by Rolf Berndt, Ralf Schmidt |
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Datensatz im Suchindex
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| author | Berndt, Rolf |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.7 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8772-4 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034887724 9783764359225 |
| issn | 0743-1643 |
| language | English |
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| spelling | Berndt, Rolf Verfasser aut Elements of the Representation Theory of the Jacobi Group by Rolf Berndt, Ralf Schmidt Basel Birkhäuser Basel 1998 1 Online-Ressource (XIII, 216 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 163 0743-1643 After Pyatetski-Shapiro [PSI] and Satake [Sal] introduced, independent of one another, an early form of the Jacobi Theory in 1969 (while not naming it as such), this theory was given a definite push by the book The Theory of Jacobi Forms by Eichler and Zagier in 1985. Now, there are some overview articles describing the developments in the theory of the Jacobi group and its automor phic forms, for instance by Skoruppa [Sk2], Berndt [Be5] and Kohnen [Ko]. We refer to these for more historical details and many more names of authors active in this theory, which stretches now from number theory and algebraic geometry to theoretical physics. But let us only briefly indicate several - sometimes very closely related - topics touched by Jacobi theory as we see it: • fields of meromorphic and rational functions on the universal elliptic curve resp. universal abelian variety • structure and projective embeddings of certain algebraic varieties and homogeneous spaces • correspondences between different kinds of modular forms • L-functions associated to different kinds of modular forms and autom- phic representations • induced representations • invariant differential operators • structure of Hecke algebras • determination of generalized Kac-Moody algebras and as a final goal related to the here first mentioned • mixed Shimura varieties and mixed motives Mathematics Group theory Number theory Number Theory Group Theory and Generalizations Mathematik Jacobi-Gruppe (DE-588)4417643-0 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 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/10.1007/978-3-0348-8772-4 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 Group theory Number theory Number Theory Group Theory and Generalizations Mathematik Jacobi-Gruppe (DE-588)4417643-0 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4417643-0 (DE-588)4148816-7 |
| 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 Group theory Number theory Number Theory Group Theory and Generalizations Mathematik Jacobi-Gruppe (DE-588)4417643-0 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Mathematics Group theory Number theory Number Theory Group Theory and Generalizations Mathematik Jacobi-Gruppe Darstellungstheorie |
| url | https://doi.org/10.1007/978-3-0348-8772-4 |
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