Partition Algebras and Kronecker Coefficients

algebraic combinatorics;representation theory;Combinatorics and Optimization

Marcott, Cameron

University of Waterloo

关键词: algebraic combinatorics;    representation theory;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/9618/3/Marcott_Cameron.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

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.