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Weyl Group Multiple Dirichlet SeriesType A Combinatorial Theory (AM-175)$
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Ben Brubaker, Daniel Bump, and Solomon Friedberg

Print publication date: 2011

Print ISBN-13: 9780691150659

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691150659.001.0001

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Type A Weyl Group Multiple Dirichlet Series

Type A Weyl Group Multiple Dirichlet Series

(p.1) Chapter One Type A Weyl Group Multiple Dirichlet Series
Weyl Group Multiple Dirichlet Series

Ben Brubaker

Daniel Bump

Solomon Friedberg

Princeton University Press

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 introduced: Φ‎, a reduced root system; n, a positive integer; F, an algebraic number field containing the group μ‎₂ₙ of 2n-th roots of unity; S, a finite set of places of F containing all the archimedean places, all places ramified over a ℚ; and an r-tuple of nonzero S-integers. In the language of representation theory, the weight of the basis vector corresponding to the Gelfand-Tsetlin pattern can be read from differences of consecutive row sums in the pattern. The chapter considers in this case expressions of the weight of the pattern up to an affine linear transformation.

Keywords:   reduced root system, Weyl group multiple Dirichlet series, archimedean place, representation theory, basis vector, Gelfand-Tsetlin pattern, row sums, affine linear transformation

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