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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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(p.54) Chapter Eight Cartoons
Weyl Group Multiple Dirichlet Series

Ben Brubaker

Daniel Bump

Solomon Friedberg

Princeton University Press

This chapter introduces a method of marking up a short Gelfand-Tsetlin pattern based on inequalities between its entries, that encodes the effect of the involution t 7 → t′ and the boxing and circling of its accordion. This will have another benefit: it will lead to the decomposition of the pattern into pieces called episodes that will ultimately lead to the reduction to the totally resonant case. The proof is easily checked using standard properties of Gauss sums. To define the cartoon, the chapter takes a slightly more formal approach to the short Gelfand-Tsetlin patterns. The vertices of the cartoon will be the elements of the substrate Θ‎, and the edges must be defined.

Keywords:   cartoon, Gelfand-Tsetlin pattern, involution, boxing, circling, accordion, episode, Gauss sum

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