Weyl group multiple drichlet series: type a combinatorial theory
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2011]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 175 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Main description: Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation |
| Beschreibung: | 1 Online-Ressource (172 S.) |
| ISBN: | 9781400838998 |
| DOI: | 10.1515/9781400838998 |
Internformat
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| 490 | 1 | |a Annals of Mathematics Studies |v number 175 | |
| 500 | |a Main description: Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation | ||
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Datensatz im Suchindex
| _version_ | 1804153276110733312 |
|---|---|
| any_adam_object | |
| author | Brubaker, Ben 1976- Bump, Daniel 1952- Friedberg, Solomon 1958- |
| author_GND | (DE-588)101372948X (DE-588)110339959 (DE-588)1014937043 |
| author_facet | Brubaker, Ben 1976- Bump, Daniel 1952- Friedberg, Solomon 1958- |
| author_role | aut aut aut |
| author_sort | Brubaker, Ben 1976- |
| author_variant | b b bb d b db s f sf |
| building | Verbundindex |
| bvnumber | BV042522883 |
| classification_rvk | SI 830 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)857968778 (DE-599)BVBBV042522883 |
| dewey-full | 515/.243 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.243 |
| dewey-search | 515/.243 |
| dewey-sort | 3515 3243 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400838998 |
| format | Electronic eBook |
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| id | DE-604.BV042522883 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:02Z |
| institution | BVB |
| isbn | 9781400838998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027957222 |
| oclc_num | 857968778 |
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| owner | DE-83 |
| owner_facet | DE-83 |
| physical | 1 Online-Ressource (172 S.) |
| psigel | ZDB-23-DGG ZDB-23-PST |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Brubaker, Ben 1976- (DE-588)101372948X aut Weyl group multiple drichlet series type a combinatorial theory Princeton, N.J. Princeton University Press [2011] © 2011 1 Online-Ressource (172 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 175 Main description: Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation Weyl-Gruppe (DE-588)4065886-7 gnd rswk-swf Dirichlet-Reihe (DE-588)4150139-1 gnd rswk-swf Dirichlet-Reihe (DE-588)4150139-1 s Weyl-Gruppe (DE-588)4065886-7 s DE-604 Bump, Daniel 1952- (DE-588)110339959 aut Friedberg, Solomon 1958- (DE-588)1014937043 aut Erscheint auch als Druck-Ausgabe 978-0-691-15065-9 Annals of Mathematics Studies number 175 (DE-604)BV040389493 175 https://doi.org/10.1515/9781400838998?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400838998&searchTitles=true Verlag Volltext |
| spellingShingle | Brubaker, Ben 1976- Bump, Daniel 1952- Friedberg, Solomon 1958- Weyl group multiple drichlet series type a combinatorial theory Annals of Mathematics Studies Weyl-Gruppe (DE-588)4065886-7 gnd Dirichlet-Reihe (DE-588)4150139-1 gnd |
| subject_GND | (DE-588)4065886-7 (DE-588)4150139-1 |
| title | Weyl group multiple drichlet series type a combinatorial theory |
| title_auth | Weyl group multiple drichlet series type a combinatorial theory |
| title_exact_search | Weyl group multiple drichlet series type a combinatorial theory |
| title_full | Weyl group multiple drichlet series type a combinatorial theory |
| title_fullStr | Weyl group multiple drichlet series type a combinatorial theory |
| title_full_unstemmed | Weyl group multiple drichlet series type a combinatorial theory |
| title_short | Weyl group multiple drichlet series |
| title_sort | weyl group multiple drichlet series type a combinatorial theory |
| title_sub | type a combinatorial theory |
| topic | Weyl-Gruppe (DE-588)4065886-7 gnd Dirichlet-Reihe (DE-588)4150139-1 gnd |
| topic_facet | Weyl-Gruppe Dirichlet-Reihe |
| url | https://doi.org/10.1515/9781400838998?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400838998&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
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