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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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Evaluation of ⋀Γ‎ and ⋀Δ‎, and Statement G

Evaluation of ⋀Γ‎ and ⋀Δ‎, and Statement G

(p.89) Chapter Fifteen Evaluation of ⋀Γ‎ and ⋀Δ‎, and Statement G
Weyl Group Multiple Dirichlet Series

Ben Brubaker

Daniel Bump

Solomon Friedberg

Princeton University Press

This chapter deals with Λ‎subscript Greek capital letter gamma and Λ‎subscript Greek capital letter delta, and Statement G. It begins by introducing a nodal signature, denoted by η‎, and a subsignature, denoted by σ‎. It then presents the proof, using the signature σ‎ to determine the rules for boxing and circling in α‎. While the circling in the accordion strictly speaking occurs at α‎ᵢ and β‎subscript i plus 1, we may equivalently consider it to occur at α‎ᵢ and β‎ᵢ for bookkeeping purposes. The chapter also considers the condition when the alternating sum for Λ‎subscript Greek capital letter gamma will only contain nonzero contributions from subsignatures.

Keywords:   nodal signature, Statement G, subsignature, boxing, circling, accordion, bookkeeping, nonzero contribution

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