Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry

We give an explicit Baxterisation formula for the fused Hecke algebra and its classical limit for the algebra of fused permutations. These algebras replace the Hecke algebra and the symmetric group in the Schur--Weyl duality theorems for the symmetrised powers of the fundamental representation of gl...

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Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: Crampe, N, L Poulain d'Andecy
Format: Article
Language:English
Subjects:
Algebra
Mathematical analysis
Matrix methods
Permutations
Representations
Symmetry
Online Access:Get full text
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Summary:We give an explicit Baxterisation formula for the fused Hecke algebra and its classical limit for the algebra of fused permutations. These algebras replace the Hecke algebra and the symmetric group in the Schur--Weyl duality theorems for the symmetrised powers of the fundamental representation of gl(N) and their quantum version. So the Baxterisation formulas presented in this paper are applicable to the \(R\)-matrices associated to these representations. In particular all "higher spins" representations of (classical and quantum) sl(2) are covered.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.05035