Partition Algebras and Kronecker Coefficients
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Date
2015-08-28
Authors
Marcott, Cameron
Journal Title
Journal ISSN
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Publisher
University of Waterloo
Abstract
Classical Schur-Weyl duality relates the representation theory of the general linear group to the representation theory of the symmetric group via their commuting actions on tensor space. With the goal of studying Kronecker products of symmetric group representations, the partition algebra is introduced as the commutator algebra of the diagonal action of the symmetric group on tensor space. An analysis of the representation theory of the partition offers results relating reduced Kronecker coefficients to Kronecker coefficients.
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Keywords
algebraic combinatorics, representation theory