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Statement B Implies Statement A

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0007
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter recalls the use of the Schützenberger involution on Gelfand-Tsetlin patterns to prove that Statement B implies Statement A. These statements will be discussed two more times in the later ... More


Outline of the Proof

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0006
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents the proof of the equivalence of the two definitions for the λ‎-parts in terms of Gelfand-Tsetlin patterns. The equivalence of these two descriptions is a deep fact that uses ... More


Statement B and Crystal Graphs

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0018
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter translates Statements A and B into Statements A′ and B′ in the language of crystal bases, and explains in this language how Statement B′ implies Statement A′. It first introduces the ... More


Statement B and the Yang-Baxter Equation

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0019
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The ... More


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