Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
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Publication:6338476
DOI10.1007/S11005-021-01436-8zbMATH Open1516.16031arXiv2004.05035MaRDI QIDQ6338476
Nicolas Crampé, Loïc Poulain d'Andecy
Publication date: 10 April 2020
Abstract: 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 -matrices associated to these representations. In particular all "higher spins" representations of (classical and quantum) sl(2) are covered.
Hecke algebras and their representations (20C08) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Yang-Baxter equations (16T25) Yang-Baxter equations and Rota-Baxter operators (17B38)
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