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Representation Theory of the Nonstandard Hecke Algebra
Journal article   Open access   Peer reviewed

Representation Theory of the Nonstandard Hecke Algebra

Jonah Blasiak
Algebras and representation theory, v 18(3), pp 585-612
2015
DOI: https://doi.org/10.1007/s10468-014-9502-y
url
http://arxiv.org/abs/1201.2209View
SubmittedOpen Access (License Unspecified),  Open

Abstract

Article Associative Rings and Algebras Commutative Rings and Algebras Mathematics Mathematics and Statistics Non-associative Rings and Algebras
The nonstandard Hecke algebra ℋ ̌ r was defined by Mulmuley and Sohoni to study the Kronecker problem. We study a quotient ℋ ̌ r , 2 of ℋ ̌ r , called the nonstandard Temperley–Lieb algebra, which is a subalgebra of the symmetric square of the Temperley–Lieb algebra TL r . We give a complete description of its irreducible representations. We find that the restriction of an irreducible ℋ ̌ r , 2 -module to ℋ ̌ r − 1 , 2 is multiplicity-free, and as a consequence, any irreducible ℋ ̌ r , 2 -module has a seminormal basis that is unique up to a diagonal transformation.

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