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- W3003177196 abstract "We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fused permutations, and its deformation is defined on a set of topological objects that we call fused braids. We use these algebras to prove a Schur–Weyl duality theorem for any tensor products of any symmetrised powers of the natural representation of Uq(glN). Then we proceed to the study of the fused Hecke algebras and in particular, we describe explicitly the irreducible representations and the branching rules. Finally, we aim to give an algebraic description of the centralisers of the tensor products of Uq(glN)-representations under consideration. We exhibit a simple explicit element that we conjecture to generate the kernel from the fused Hecke algebra to the centraliser. We prove this conjecture in some cases and in particular, we obtain a description of the centraliser of any tensor products of any finite-dimensional representations of Uq(sl2)." @default.
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- W3003177196 date "2022-02-28" @default.
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- W3003177196 title "Fused Braids and Centralisers of Tensor Representations of Uq(glN)" @default.
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- W3003177196 doi "https://doi.org/10.1007/s10468-022-10116-7" @default.
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