In [l], we proved a criterion for the disjointness of two induced representations UL and UM of a Lie group G, where L and M are finite-dimensional unitary representations of compact subgroups H and R, respectively, of G. The purpose of this paper is to improve this theorem by getting a stronger conclusion, while dropping the conditions that G be a Lie group and H be compact, and that L and M he...

Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra H, we construct an induced Hopf representation from a representation of a bialgebra B using a bialgebra epimorphism π : H → B. Application on the quantum group Eq(2) is given. Mathematics Subject Classification: 16T05, 06B15, 17B37

Let K/F be a quadratic extension of p-adic fields, σ the nontrivial element of the Galois group of K over F , and ∆ a quasi-square-integrable representation of GL(n,K). Denoting by ∆∨ the smooth contragredient of ∆, and by ∆σ the representation ∆ ◦ σ, we show that representation ofGL(2n,K) obtained by normalized parabolic induction of the representation ∆∨⊗∆σ, is distinguished with respect to G...