Logo image
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
url
http://arxiv.org/abs/1201.2209View

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.

Metrics

6 Record Views
1 citations in Scopus

Details

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Web of Science research areas
Mathematics
Logo image