Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut(N) of N. It is well-known that if (K⋉ N, K) is a Gelfand pair then N is at most 2-step nilpotent Lie group. The notion of Gelfand pair ...

Let H_n be the 2n + 1-dimensional Heisenberg group. We consider thegeneralized Gelfand pairs (R*xH_1,R) and ((R_{>0} ×SO(n))xH_n, R_?>0? ×SO(n)) for n ≥ 2.We describe the spherical distributions corresponding to these ...

We present a simplified way to construct the Gelfand-Tsetlin modules over gl(n,C) related to a 1-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic ...

In this work, we consider a family of Gelfand pairs (KnN, N) (inshort (K, N) ) where Nis a two step nilpotent Lie group, and Kis the group oforthogonal automorphisms ofN. This family has a nice analytic property: almos ...

Esta tesis se encuadra en el estudio del análisis armónico en pares de Gelfand de la forma (K,N), donde N es un grupo de Lie nilpotente y K es un subgrupo de automorfismos de N. En una primera parte trabajamos con una ...

We present a method to obtain infinitely many examples of pairs (W, D) consisting of a matrix weight W in one variable and a symmetric second-order differential operator D. The method is based on a uniform construction of ...

We denote by $H_{n}$ the $2n+1$-dimensional Heisenberg group and study the spherical transform associated with the generalized Gelfand pair $(U(p,q) \rtimes H_{n},U(p,q))$, $p+q=n$, which is defined on the space of Schwartz ...

In this article, using the notion of group contraction, we obtain the spherical functions of the strong Gelfand pair (M(n),SO(n)) as an appropriate limit of spherical functions of the strong Gelfand pair (SO(n+1),SO(n)) ...

We consider R3 as a homogeneous manifold for the action of the motion group given by rotations and translations. For an arbitrary τ∈ SO(3) ^ , let Eτ be the homogeneous vector bundle over R3 associated with τ. An interesting ...

Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the ...