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- W4381569481 abstract "This paper gives an algebraic presentation of the fused Hecke algebra which describes the centraliser of tensor products of the $U_q(gl_N)$-representation labelled by a one-row partition of any size with vector representations. It is obtained through a detailed study of a new algebra that we call the symmetric one-boundary Hecke algebra. In particular, we prove that the symmetric one-boundary Hecke algebra is free over a ring of Laurent polynomials in three variables and we provide a basis indexed by a certain subset of signed permutations. We show how the symmetric one-boundary Hecke algebra admits the one-boundary Temperley-Lieb algebra as a quotient, and we also describe a basis of this latter algebra combinatorially in terms of signed permutations with avoiding patterns. The quotients corresponding to any value of $N$ in $gl_N$ (the Temperley-Lieb one corresponds to $N=2$) are also introduced. Finally, we obtain the fused Hecke algebra, and in turn the centralisers for any value of $N$, by specialising and quotienting the symmetric one-boundary Hecke algebra. In particular, this generalises to the Hecke case the description of the so-called boundary seam algebra, which is then obtained (taking $N=2$) as a quotient of the fused Hecke algebra." @default.
- W4381569481 created "2023-06-22" @default.
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- W4381569481 date "2023-06-19" @default.
- W4381569481 modified "2023-10-18" @default.
- W4381569481 title "Fused Hecke algebra and one-boundary algebras" @default.
- W4381569481 doi "https://doi.org/10.48550/arxiv.2306.10937" @default.
- W4381569481 hasPublicationYear "2023" @default.
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