Cell structures for the Yokonuma-Hecke algebra and the algebra of braids and ties

Abstract

We construct a faithful tensor representation for the Yokonuma-Hecke algebra Y, and use it to give a concrete isomorphism between Y and Shoji's modified Ariki-Koike algebra. We give a cellular basis for Y and show that the Jucys-Murphy elements for Y are JM-elements in the abstract sense. Finally, we construct a cellular basis for the Aicardi-Juyumaya algebra of braids and ties.

49 pages. Final version

References in corpus (1)

• The HOMFLYPT polynomials of sublinks and the Yokonuma-Hecke algebras

Cited by in corpus (11)

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• Affine cellularity of affine Yokonuma-Hecke algebras
• An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications
• A bt-algebra of type B
• Representations of $0$-Yokonuma-Hecke algebras
• Clifford theory for Yokonuma--Hecke algebras and deformation of complex reflection groups
• Yokonuma-Schur algebras
• A categorical equivalence between affine Yokonuma-Hecke algebras and some quiver Hecke algebras
• Framization of Schur--Weyl duality and Yokonuma--Hecke type algebras
• An Iwahori-Matsumoto presentation of affine Yokonuma-Hecke algebras
• Calibrated representations of affine Yokonuma-Hecke algebras