A crystal definition for symplectic multiple dirichlet series

Jennifer Beineke; Ben Brubaker; Sharon Frechette

doi:10.1007/978-0-8176-8334-4_2

A crystal definition for symplectic multiple dirichlet series

Jennifer Beineke, Ben Brubaker, Sharon Frechette

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

5 Scopus citations

Abstract

We present a definition for Weyl group multiple Dirichlet series (MDS) of Cartan type C, where the coefficients of the series are given by statistics on crystal graphs for certain highest-weight representations of Sp(2r, C). In earlier work (Beineke et al., Pacific J. Math., 2011), we presented a definition based on Gelfand-Tsetlin patterns, and the equivalence of the two definitions is explained here. Finally, we demonstrate how to prove analytic continuation and functional equations for any multiple Dirichlet series with fixed data by reduction to rank one information. This method is amenable to MDS of all types.

Original language	English (US)
Title of host publication	Multiple Dirichlet Series, L-functions and Automorphic Forms
Publisher	Birkhauser Boston
Pages	37-63
Number of pages	27
ISBN (Electronic)	9780817683344
ISBN (Print)	9780817683337
DOIs	https://doi.org/10.1007/978-0-8176-8334-4_2
State	Published - Jan 1 2012

Bibliographical note

Publisher Copyright:
© 2012 Springer Science+Business Media, LLC. All rights reserved.

Keywords

Crystal graph
Gelfand-tsetlin pattern
Littelmann polytope
Weylgroup multiple Dirichlet series
Whittaker function

Publisher link

10.1007/978-0-8176-8334-4_2

Find It

Find It at U of M Libraries

Cite this

@inbook{6e346095331e46458d3e4a996aaa3e3d,

title = "A crystal definition for symplectic multiple dirichlet series",

abstract = "We present a definition for Weyl group multiple Dirichlet series (MDS) of Cartan type C, where the coefficients of the series are given by statistics on crystal graphs for certain highest-weight representations of Sp(2r, C). In earlier work (Beineke et al., Pacific J. Math., 2011), we presented a definition based on Gelfand-Tsetlin patterns, and the equivalence of the two definitions is explained here. Finally, we demonstrate how to prove analytic continuation and functional equations for any multiple Dirichlet series with fixed data by reduction to rank one information. This method is amenable to MDS of all types.",

keywords = "Crystal graph, Gelfand-tsetlin pattern, Littelmann polytope, Weylgroup multiple Dirichlet series, Whittaker function",

author = "Jennifer Beineke and Ben Brubaker and Sharon Frechette",

year = "2012",

month = jan,

day = "1",

doi = "10.1007/978-0-8176-8334-4_2",

language = "English (US)",

isbn = "9780817683337",

pages = "37--63",

booktitle = "Multiple Dirichlet Series, L-functions and Automorphic Forms",

publisher = "Birkhauser Boston",

}

TY - CHAP

T1 - A crystal definition for symplectic multiple dirichlet series

AU - Beineke, Jennifer

AU - Brubaker, Ben

AU - Frechette, Sharon

PY - 2012/1/1

Y1 - 2012/1/1

N2 - We present a definition for Weyl group multiple Dirichlet series (MDS) of Cartan type C, where the coefficients of the series are given by statistics on crystal graphs for certain highest-weight representations of Sp(2r, C). In earlier work (Beineke et al., Pacific J. Math., 2011), we presented a definition based on Gelfand-Tsetlin patterns, and the equivalence of the two definitions is explained here. Finally, we demonstrate how to prove analytic continuation and functional equations for any multiple Dirichlet series with fixed data by reduction to rank one information. This method is amenable to MDS of all types.

AB - We present a definition for Weyl group multiple Dirichlet series (MDS) of Cartan type C, where the coefficients of the series are given by statistics on crystal graphs for certain highest-weight representations of Sp(2r, C). In earlier work (Beineke et al., Pacific J. Math., 2011), we presented a definition based on Gelfand-Tsetlin patterns, and the equivalence of the two definitions is explained here. Finally, we demonstrate how to prove analytic continuation and functional equations for any multiple Dirichlet series with fixed data by reduction to rank one information. This method is amenable to MDS of all types.

KW - Crystal graph

KW - Gelfand-tsetlin pattern

KW - Littelmann polytope

KW - Weylgroup multiple Dirichlet series

KW - Whittaker function

UR - http://www.scopus.com/inward/record.url?scp=85026223717&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026223717&partnerID=8YFLogxK

U2 - 10.1007/978-0-8176-8334-4_2

DO - 10.1007/978-0-8176-8334-4_2

M3 - Chapter

AN - SCOPUS:85026223717

SN - 9780817683337

SP - 37

EP - 63

BT - Multiple Dirichlet Series, L-functions and Automorphic Forms

PB - Birkhauser Boston

ER -

A crystal definition for symplectic multiple dirichlet series

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this