A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
Let \(G_{n,r}=(\mathbb{Z}/r\mathbb{Z})\wr S_n\) be the wreath product of \(\mathbb{Z}/r\mathbb{Z}\) with \(S_n\). In this paper, the structure of the generic Hecke algebra \(H_{n,r}\) of \(G_{n,r}\) over the algebra \(A_0=\mathbb{Z}[q,q^{-1},u_1,\dots,u_r]\) is studied and the irreducible representations of \(G_{n,r}\) over the quotient field \(K_0\) of \(A_0\) are classified. When we specify \(r\) and \(u_1\) in \(H_{n,r}\) one gets the generic Hecke algebra of type \(A_n\) and \(B_n\). So the results of this paper can be applied to the Hecke algebras \(A_n\) and \(B_n\) as special cases. In particular the centre of \(H_{n,r}\) is given explicitly.
scientific article; zbMATH DE number 638527