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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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The Reduction to Statement D

The Reduction to Statement D

Chapter:
(p.77) Chapter Thirteen The Reduction to Statement D
Source:
Weyl Group Multiple Dirichlet Series
Author(s):

Ben Brubaker

Daniel Bump

Solomon Friedberg

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691150659.003.0013

This chapter focuses on the language of resotopes and assumes that γ‎Lsubscript Greek small letter epsilon and γ‎Rsubscript Greek small letter epsilon are multiples of n for every totally resonant episode. It also recalls that s and d are the weights of the accordions under consideration. It begins with the proposition that Statement D is equivalent to Statement C, and that Statement D is true if ns. It then describes the case of a totally resonant short Gelfand-Tsetlin pattern before presenting the proof that Statement D implies Statement B. It shows that the reduction to Statement D is straightforward for Class I, but each of the remaining classes involves some nuances.

Keywords:   resotope, episode, accordion, Statement D, Statement C, Gelfand-Tsetlin pattern, Statement B, Class I

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