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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Matching polytopes and Specht modules
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by Ricky Ini Liu PDF
Trans. Amer. Math. Soc. 364 (2012), 1089-1107 Request permission

Abstract:

We prove that the dimension of the Specht module of a forest $G$ is the same as the normalized volume of the matching polytope of $G$. We also associate to $G$ a symmetric function $s_G$ (analogous to the Schur symmetric function $s_\lambda$ for a partition $\lambda$) and investigate its combinatorial and representation-theoretic properties in relation to the Specht module and Schur module of $G$. We then use this to define notions of standard and semistandard tableaux for forests.
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Additional Information
  • Ricky Ini Liu
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Email: riliu@math.mit.edu, riliu@umich.edu
  • Received by editor(s): October 7, 2010
  • Received by editor(s) in revised form: November 29, 2010
  • Published electronically: October 4, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 1089-1107
  • MSC (2010): Primary 05E10
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05516-9
  • MathSciNet review: 2846364