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In [Lu6] Lusztig defined a certain algebra $H,$ which is a direct sum of various algebras $H_{mathfrak{o}}.$ We establish an explicit algebra isomorphism between each algebra $H_{mathfrak{o}}$ and some matrix algebra with coefficients in the tensor product of an (affine or finite) Hecke algebra and a group algebra. We give an application.
Inspired by the work [PA], we establish an explicit algebra isomorphism between the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q)$ and a direct sum of matrix algebras over tensor products of degenerate cyclotomic Hecke algebras of type
The cyclotomic Birman-Murakami-Wenzl (BMW) algebras B_n^k, introduced by R. Haring-Oldenburg, are a generalisation of the BMW algebras associated with the cyclotomic Hecke algebras of type G(k,1,n) (aka Ariki-Koike algebras) and type B knot theory.
In cite{CK2005} and cite{Hubery2005}, the authors proved the cluster multiplication theorems for finite type and affine type. We generalize their results and prove the cluster multiplication theorem for arbitrary type by using the properties of 2--Ca
Let $(bf U, bf U^imath)$ be a quantum symmetric pair of Kac-Moody type. The $imath$quantum groups $bf U^imath$ and the universal $imath$quantum groups $widetilde{bf U}^imath$ can be viewed as a generalization of quantum groups and Drinfeld doubles $w
Let T_n be the maximal torus of diagonal matrices in GL_n, t_n be the Lie algebra of T_n and let N_n=N_{GL_n}(T_n) be the normalizer of T_n in GL_n. Consider then the quotient stacks [t_n/N_n] and [gl_n/GL_n] for the conjugation actions. In this pape