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19
On the characteristic map of finite unitary groups
 Adv. Math
"... In his seminal work [8], Green described a remarkable connection between the class functions of the finite general linear group GL(n, Fq) and a generalization of the ring of symmetric functions of the symmetric group Sn. In particular, Green defines a map, called the characteristic map, that takes ..."
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In his seminal work [8], Green described a remarkable connection between the class functions of the finite general linear group GL(n, Fq) and a generalization of the ring of symmetric functions of the symmetric group Sn. In particular, Green defines a map, called the characteristic map, that takes
A GELFAND MODEL FOR WREATH PRODUCTS
, 802
"... Abstract. A Gelafand model for wreath products Zr ≀ Sn is constructed. The proof relies on a combinatorial interpretation of the characters of the model, extending a classical result of Frobenius and Schur. 1. ..."
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Abstract. A Gelafand model for wreath products Zr ≀ Sn is constructed. The proof relies on a combinatorial interpretation of the characters of the model, extending a classical result of Frobenius and Schur. 1.
Involution models of finite Coxeter groups
"... Abstract. Let G be a finite Coxeter group. Using previous results on Weyl groups, and covering the cases of noncrystallographic groups, we show that G has an involution model if and only if all of its irreducible factors are of type An, Bn, D2n+1, H3, or I2(n). ..."
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Abstract. Let G be a finite Coxeter group. Using previous results on Weyl groups, and covering the cases of noncrystallographic groups, we show that G has an involution model if and only if all of its irreducible factors are of type An, Bn, D2n+1, H3, or I2(n).
Twisted FrobeniusSchur indicators of finite symplectic groups
 J. Algebra
"... In [8], R. Gow proves the following theorem. Theorem 1.1. Let G = GL(n,Fq), where q is odd. Let G+ be the split extension of G by the transposeinverse automorphism. That is, G+ = 〈G, τ  τ2 = 1, τ−1gτ = tg−1 for all g ∈ G〉. ..."
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In [8], R. Gow proves the following theorem. Theorem 1.1. Let G = GL(n,Fq), where q is odd. Let G+ be the split extension of G by the transposeinverse automorphism. That is, G+ = 〈G, τ  τ2 = 1, τ−1gτ = tg−1 for all g ∈ G〉.
Twisted FrobeniusSchur indicators for Hopf algebras
 ISSN 00218693. doi:10.1016/j.jalgebra.2011.12.026. URL http://dx.doi.org/10.1016/j.jalgebra.2011.12.026
, 2012
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Involutions acting on representations
 Department of Mathematics and Statistics American University
"... For a group G with order 2 automorphism ι, we consider irreducible representations (pi, V) of G such that ιpi ∼ = p̂i, where p̂i is the contragredient representation of pi. This isomorphism gives rise to a nondegenerate bilinear form on V which is (pi, ιpi)invariant, unique up to scalar, and conse ..."
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Cited by 3 (2 self)
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For a group G with order 2 automorphism ι, we consider irreducible representations (pi, V) of G such that ιpi ∼ = p̂i, where p̂i is the contragredient representation of pi. This isomorphism gives rise to a nondegenerate bilinear form on V which is (pi, ιpi)invariant, unique up to scalar, and consequently is
WREATH PRODUCT GENERALIZATIONS OF THE TRIPLE (S2n, Hn, ϕ) AND THEIR SPHERICAL FUNCTIONS HIROSHI MIZUKAWA
, 908
"... Abstract. The symmetric group S2n and the hyperoctaheadral group Hn is a Gelfand triple for an arbitrary linear representation ϕ of Hn. Their ϕspherical functions can be caught as transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wr ..."
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Abstract. The symmetric group S2n and the hyperoctaheadral group Hn is a Gelfand triple for an arbitrary linear representation ϕ of Hn. Their ϕspherical functions can be caught as transition matrix between suitable symmetric functions and the power sums. We generalize this triplet in the term of wreath product. It is shown that our triplet are always to be a Gelfand triple. Furthermore we study the relation between their spherical functions and multipartition version of the ring of symmetric functions.