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THE POLYTABLOID BASIS EXPANDS POSITIVELY INTO THE WEB BASIS

Part of: Algebraic combinatorics

Published online by Cambridge University Press:  19 August 2019

BRENDON RHOADES
BRENDON RHOADES*
Affiliation:
Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA; bprhoades@math.ucsd.edu

Abstract

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We show that the transition matrix from the polytabloid basis to the web basis of the irreducible $\mathfrak{S}_{2n}$-representation of shape $(n,n)$ has nonnegative integer entries. This proves a conjecture of Russell and Tymoczko [Int. Math. Res. Not., 2019(5) (2019), 1479–1502].

MSC classification

Primary: 05E10: Combinatorial aspects of representation theory
Secondary: 05E40: Combinatorial aspects of commutative algebra
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 7 , 2019 , e26
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author 2019

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