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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Matching polytopes and Specht modules


Author: Ricky Ini Liu
Journal: Trans. Amer. Math. Soc. 364 (2012), 1089-1107
MSC (2010): Primary 05E10
Published electronically: October 4, 2011
MathSciNet review: 2846364
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05516-9
Received by editor(s): October 7, 2010
Received by editor(s) in revised form: November 29, 2010
Published electronically: October 4, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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