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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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Snakes

Snakes

Chapter:
(p.58) Chapter Nine Snakes
Source:
Weyl Group Multiple Dirichlet Series
Author(s):

Ben Brubaker

Daniel Bump

Solomon Friedberg

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691150659.003.0009

This chapter introduces the “Snake Lemma” and uses it to prove the statement that GΓ‎(t) = GΔ‎(t′) is “often” true. It first describes an indexing of the Γ‎ preaccordion and of the Δ‎′ preaccordion; each indexing visits the episodes of the sequence in order from left to right, and after it is finished with an episode, it moves on to the next with no skipping around. Thus both indexings must be in the same episode. If there are resonances, there will be more than one possible pair of snakes. These are obtained through a process of specialization described in the proof. Any one of these pairs of snakes are considered canonical.

Keywords:   snakes, Snake Lemma, preaccordion, indexing, episode, resonance

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