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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.67) Chapter Eleven Types
Weyl Group Multiple Dirichlet Series

Ben Brubaker

Daniel Bump

Solomon Friedberg

Princeton University Press

This chapter divides the prototypes into much smaller units called types. It fixes a top and bottom row, and therefore a cartoon. For each episode ε‎ of the cartoon, the chapter fixes an integer κ‎subscript Greek small letter epsilon. Then the set of all short Gelfand-Tsetlin patterns with the given top and bottom rows is called a type. Thus two patterns are in the same type if and only if they have the same top and bottom rows (and hence the same cartoon), and if the sum of the first (middle) row elements in each episode is the same for both patterns. The possible episodes may be grouped into four classes: Class I, II, III, and IV.

Keywords:   prototype, type, cartoon, episode, Gelfand-Tsetlin pattern, class

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