Zonal spherical functions on the complex reflection groups and (n+1,m+1)-hypergeometric functions

Mizukawa, Hiroshi

doi:10.1016/s0001-8708(03)00092-6

Cited by 24 publications

(29 citation statements)

References 7 publications

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“…Also, Akazawa and Mizukawa [1] obtained a similar result for the pair (D(r, n), D (1, n)), where D(r, n) = D r S n is the wreath product of the dihedral group of order 2r and S n . Since the Hecke algebra of any Gelfand pair is a character algebra, our result includes all the cases dealt with in [10,1] (see Remark 2.1).…”

Section: Hiroshi Mizukawa and Hajime Tanakamentioning

confidence: 92%

“…In [10], the first author showed that the Gelfand pair (G(r, 1, n), S n ) gives rise to orthogonal polynomials expressed by (r, 2r)-hypergeometric functions, where S n and G(r, 1, n) ∼ = (Z/rZ) S n denote the symmetric group of degree n and the imprimitive complex reflection group, respectively. Also, Akazawa and Mizukawa [1] obtained a similar result for the pair (D(r, n), D (1, n)), where D(r, n) = D r S n is the wreath product of the dihedral group of order 2r and S n .…”

Section: Hiroshi Mizukawa and Hajime Tanakamentioning

confidence: 99%

“…If A is the Hecke algebra of a Gelfand pair (G, H), then S n (A) coincides with that of the Gelfand pair (G S n , H S n ) (see [10,1]). In particular, when G = S q and H = S q−1 , S n (A) is the Bose-Mesner algebra of the Hamming association scheme H(n, q).…”

Section: In the Above Equations Conventionally We Putmentioning

confidence: 99%

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(𝑛+1,𝑚+1)-hypergeometric functions associated to character algebras

Mizukawa

Tanaka

2004

Proc. Amer. Math. Soc.

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Section: Hiroshi Mizukawa and Hajime Tanakamentioning

confidence: 92%

Section: Hiroshi Mizukawa and Hajime Tanakamentioning

confidence: 99%

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(𝑛+1,𝑚+1)-hypergeometric functions associated to character algebras

Mizukawa

Tanaka

2004

Proc. Amer. Math. Soc.

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“…Remark 3.6. The monomial symmetric functions appear as S n -invariants in irreducible components of 1 G(r, 1, n) S n (see [6]). …”

Section: Proposition 35mentioning

confidence: 99%

“…[6]). Because their zonal sperical functions have multivariate hypergeometric expression, we are interested in this pair.…”

Section: Introductionmentioning

confidence: 99%

Twisted Gelfand Pairs of Complex Reflection Groups and r-Congruence Properties of Schur Functions

Mizukawa

2011

Ann. Comb.

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Preliminaries

Ceccherini‐Silberstein¹,

Scarabotti²,

Tolli³

2020

Lecture Notes in Mathematics

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Zonal spherical functions on the complex reflection groups and (n+1,m+1)-hypergeometric functions

Cited by 24 publications

References 7 publications

(𝑛+1,𝑚+1)-hypergeometric functions associated to character algebras

(𝑛+1,𝑚+1)-hypergeometric functions associated to character algebras

Twisted Gelfand Pairs of Complex Reflection Groups and r-Congruence Properties of Schur Functions

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