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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.74) Chapter Twelve Knowability
Weyl Group Multiple Dirichlet Series

Ben Brubaker

Daniel Bump

Solomon Friedberg

Princeton University Press

This chapter introduces the Knowability Lemma, which explains when products of Gauss sums associated to elements of a preaccordion are explicitly evaluable as polynomials in q, the order of the residue class field. It considers an episode in the cartoon associated to the short Gelfand-Tsetlin pattern and the three cases that apply according to the Knowability Lemma, two of which are maximality and knowability. Knowability is not important for the proof that Statement C implies Statement B. The chapter discusses the cases where ε‎ is Class II or Class I, leaving the remaining two cases to the reader. It also describes the variant of the argument for the case that ε‎ is of Class I, again leaving the two other cases to the reader.

Keywords:   knowability, Knowability Lemma, Gauss sum, preaccordion, polynomial, residue class field, episode, cartoon, Gelfand-Tsetlin pattern, maximality

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