ON GELFAND PAIR OVER HYPERGROUPS

2021 ◽  
Vol 132 (1) ◽  
pp. 63-76
Author(s):  
Brou Kouakou Germain ◽  
Kangni Kinvi
Keyword(s):  
Gelfand Pair

scholarly journals (U(p, q), U(p − 1, q)) is a generalized Gelfand pair

2008 ◽  
Vol 261 (3) ◽  
pp. 525-529 ◽  
Author(s):  
Gerrit van Dijk
Keyword(s):  
Gelfand Pair

scholarly journals $$(O(V \oplus F), O(V))$$ is a Gelfand pair for any quadratic space V over a local field F

2008 ◽  
Vol 261 (2) ◽  
pp. 239-244 ◽  
Author(s):  
Avraham Aizenbud ◽  
Dmitry Gourevitch ◽  
Eitan Sayag
Keyword(s):  
Local Field ◽  
Quadratic Space ◽  
Gelfand Pair

Partial Characters and Signed Quotient Hypergroups

1999 ◽  
Vol 51 (1) ◽  
pp. 96-116 ◽  
Author(s):  
Margit Rösler ◽  
Michael Voit
Keyword(s):  
Heisenberg Group ◽  
Closed Subgroup ◽  
Gelfand Pair ◽  
Coset Space ◽  
Commutative Hypergroup

AbstractIfGis a closed subgroup of a commutative hypergroupK, then the coset spaceK/Gcarries a quotient hypergroup structure. In this paper, we study related convolution structures onK/Gcoming fromdeformations of the quotient hypergroup structure by certain functions onKwhich we call partial characters with respect toG. They are usually not probability-preserving, but lead to so-called signed hypergroups onK/G. A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair (U(n, 1),U(n)) are discussed.

Strong Gelfand pairs of symmetric groups

2020 ◽  
pp. 2150054
Author(s):  
Gradin Anderson ◽  
Stephen P. Humphries ◽  
Nathan Nicholson
Keyword(s):  
Commutative Ring ◽  
Finite Groups ◽  
Symmetric Groups ◽  
Maximal Dimension ◽  
Gelfand Pair ◽  
Gelfand Pairs ◽  
Schur Ring

A strong Gelfand pair is a pair [Formula: see text], of finite groups such that the Schur ring determined by the [Formula: see text]-classes [Formula: see text], is a commutative ring. We find all strong Gelfand pairs [Formula: see text]. We also define an extra strong Gelfand pair [Formula: see text], this being a strong Gelfand pair of maximal dimension, and show that in this case [Formula: see text] must be abelian.

Gelfand pair associated with a hoph algebra and a coideal

1994 ◽  
Vol 46 (8) ◽  
pp. 1157-1171
Author(s):  
Yu. A. Chapovskii
Keyword(s):  
Gelfand Pair

scholarly journals Corwin–Greenleaf multiplicity function for compact extensions of the Heisenberg group

2018 ◽  
Vol 29 (09) ◽  
pp. 1850056
Author(s):  
Majdi Ben Halima ◽  
Anis Messaoud
Keyword(s):  
Heisenberg Group ◽  
Lie Algebras ◽  
Closed Subgroup ◽  
Sufficient Conditions ◽  
Multiplicity Function ◽  
Coadjoint Orbits ◽  
Gelfand Pair ◽  
Irreducible Unitary Representations ◽  
Multiplicity Formula ◽  
The Relationship

Let [Formula: see text] be the [Formula: see text]-dimensional Heisenberg group and [Formula: see text] a closed subgroup of [Formula: see text] acting on [Formula: see text] by automorphisms such that [Formula: see text] is a Gelfand pair. Let [Formula: see text] be the semidirect product of [Formula: see text] and [Formula: see text]. Let [Formula: see text] be the respective Lie algebras of [Formula: see text] and [Formula: see text], and [Formula: see text] the natural projection. For coadjoint orbits [Formula: see text] and [Formula: see text], we denote by [Formula: see text] the number of [Formula: see text]-orbits in [Formula: see text], which is called the Corwin–Greenleaf multiplicity function. In this paper, we give two sufficient conditions on [Formula: see text] in order that [Formula: see text] For [Formula: see text], assuming furthermore that [Formula: see text] and [Formula: see text] are admissible and denoting respectively by [Formula: see text] and [Formula: see text] their corresponding irreducible unitary representations, we also discuss the relationship between [Formula: see text] and the multiplicity [Formula: see text] of [Formula: see text] in the restriction of [Formula: see text] to [Formula: see text]. Especially, we study in Theorem 4 the case where [Formula: see text]. This inequality is interesting because we expect the equality as the naming of the Corwin–Greenleaf multiplicity function suggests.

On the symmetric Gelfand pair (ℋn ×ℋn−1,diag(ℋn−1))

2020 ◽  
pp. 2150085
Author(s):  
Omar Tout
Keyword(s):  
Representation Formula ◽  
Conjugacy Classes ◽  
Gelfand Pair ◽  
Induced Representation ◽  
Hyperoctahedral Group ◽  
Multiplicity Free

We show that the [Formula: see text]-conjugacy classes of [Formula: see text] where [Formula: see text] is the hyperoctahedral group on [Formula: see text] elements, are indexed by marked bipartitions of [Formula: see text] This will lead us to prove that [Formula: see text] is a symmetric Gelfand pair and that the induced representation [Formula: see text] is multiplicity free.

scholarly journals Gelfand Pairs Involving the Wreath Product of Finite Abelian Groups with Symmetric Groups

2020 ◽  
pp. 1-7
Author(s):  
Omar Tout
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Wreath Product ◽  
Abelian Groups ◽  
Symmetric Groups ◽  
Gelfand Pair ◽  
Gelfand Pairs ◽  
Finite Abelian Groups ◽  
A Finite Group

Abstract It is well known that the pair $(\mathcal {S}_n,\mathcal {S}_{n-1})$ is a Gelfand pair where $\mathcal {S}_n$ is the symmetric group on n elements. In this paper, we prove that if G is a finite group then $(G\wr \mathcal {S}_n, G\wr \mathcal {S}_{n-1}),$ where $G\wr \mathcal {S}_n$ is the wreath product of G by $\mathcal {S}_n,$ is a Gelfand pair if and only if G is abelian.

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