A crystal definition for symplectic multiple Dirichlet series
This paper presents a definition for a family of Weyl group multiple Dirichlet series (henceforth \MDS") of Cartan type C using a combinatorial model for crystal bases due to Berenstein-Zelevinsky [2] and Littelmann [12]. Recall that a Weyl group MDS is a Dirichlet series in several complex var...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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Birkhauser Boston
2012
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| Online Access: | http://hdl.handle.net/1721.1/71257 |
| _version_ | 1826204701810491392 |
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| author | Beineke, Jennifer Brubaker, Benjamin Brock Frechette, Sharon |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Beineke, Jennifer Brubaker, Benjamin Brock Frechette, Sharon |
| author_sort | Beineke, Jennifer |
| collection | MIT |
| description | This paper presents a definition for a family of Weyl group multiple Dirichlet series (henceforth \MDS") of Cartan type C using a combinatorial model for crystal bases due to Berenstein-Zelevinsky [2] and Littelmann [12]. Recall that a Weyl group MDS is a Dirichlet series in several complex variables which (at least conjecturally) possesses analytic continuation to a meromorphic function and satisfies functional equations whose action on the complex space is isomorphic to the given Weyl group. In [1], we presented a definition for such a series in terms of a basis for highest weight representations of Sp(2r;C) { Type C Gelfand-Tsetlin patterns { and proved that the series satisfied the conjectured analytic properties in a number of special cases. Here we recast that definition in the language of crystal bases and find that the resulting MDS, whose form appears as an unmotivated miracle in the language of Gelfand-Tsetlin patterns, is more naturally defined in this new language. |
| first_indexed | 2024-09-23T12:59:41Z |
| format | Article |
| id | mit-1721.1/71257 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:59:41Z |
| publishDate | 2012 |
| publisher | Birkhauser Boston |
| record_format | dspace |
| spelling | mit-1721.1/712572022-09-28T11:21:00Z A crystal definition for symplectic multiple Dirichlet series Beineke, Jennifer Brubaker, Benjamin Brock Frechette, Sharon Massachusetts Institute of Technology. Department of Mathematics Brubaker, Benjamin Brock Brubaker, Benjamin Brock Frechette, Sharon Beineke, Jennifer This paper presents a definition for a family of Weyl group multiple Dirichlet series (henceforth \MDS") of Cartan type C using a combinatorial model for crystal bases due to Berenstein-Zelevinsky [2] and Littelmann [12]. Recall that a Weyl group MDS is a Dirichlet series in several complex variables which (at least conjecturally) possesses analytic continuation to a meromorphic function and satisfies functional equations whose action on the complex space is isomorphic to the given Weyl group. In [1], we presented a definition for such a series in terms of a basis for highest weight representations of Sp(2r;C) { Type C Gelfand-Tsetlin patterns { and proved that the series satisfied the conjectured analytic properties in a number of special cases. Here we recast that definition in the language of crystal bases and find that the resulting MDS, whose form appears as an unmotivated miracle in the language of Gelfand-Tsetlin patterns, is more naturally defined in this new language. 2012-06-28T18:06:18Z 2012-06-28T18:06:18Z 2012-07 Article http://purl.org/eprint/type/BookItem 978-0-8176-8333-7 http://hdl.handle.net/1721.1/71257 Beineke, Jennifer, Ben Brubaker and Sharon Frechette. "A crystal definition for symplectic multiple Dirichlet series." Chapter 2 in Multiple Dirichlet Series, L-functions and Automorphic Forms, Eds, Daniel Bump, Solomon Friedberg, and Dorian Goldfeld, Springer Science+Business Media, LLC 2012 (Series: Progress in Mathematics, vol. 300. July 31, 2012). en_US http://www.springer.com/birkhauser/mathematics/book/978-0-8176-8333-7 Progress in Mathematics, vol. 300, 2012 Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Birkhauser Boston MIT web domain |
| spellingShingle | Beineke, Jennifer Brubaker, Benjamin Brock Frechette, Sharon A crystal definition for symplectic multiple Dirichlet series |
| title | A crystal definition for symplectic multiple Dirichlet series |
| title_full | A crystal definition for symplectic multiple Dirichlet series |
| title_fullStr | A crystal definition for symplectic multiple Dirichlet series |
| title_full_unstemmed | A crystal definition for symplectic multiple Dirichlet series |
| title_short | A crystal definition for symplectic multiple Dirichlet series |
| title_sort | crystal definition for symplectic multiple dirichlet series |
| url | http://hdl.handle.net/1721.1/71257 |
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