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Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Ben Brubaker, Daniel Bump, and Solomon Friedberg

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

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, ... More


Type A Weyl Group Multiple Dirichlet Series

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter describes Type A Weyl group multiple Dirichlet series. It begins by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, the following parameters are ... More


Whittaker Functions

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0004
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter shows that Weyl group multiple Dirichlet series are expected to be Whittaker coefficients of metaplectic Eisenstein series. The fact that Whittaker coefficients of Eisenstein series ... More


Crystals and Gelfand-Tsetlin Patterns

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0002
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter translates the definitions of the Weyl group multiple Dirichlet series into the language of crystal bases. It reinterprets the entries in these arrays and the accompanying boxing and ... More


Statement B and the Yang-Baxter Equation

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0019
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The ... More


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