Gelfand Transforms of So(3)-invariant Schwartz Functions on the Free Nilpotent Group N3,2 Véronique Fischer and Fulvio Ricci

The Space of Bounded Spherical Functions on the Free Two Step Nilpotent Lie Group

Let N be a connected and simply connected 2-step nilpotent Lie group and K be a compact subgroup of Aut(N). We say that (K,N) is a Gelfand pair when the set of integrable K-invariant functions on N forms an abelian algebra under convolution. In this paper, we construct a one-to-one correspondence between the set ∆(K, N) of bounded spherical functions for such a Gelfand pair and a set A(K, N) of...

The Orbit Method and Gelfand Pairs Associated with Nilpotent Lie Groups

Let K be a compact Lie group acting by automorphisms on a nilpotent Lie group N . One calls (K,N) a Gelfand pair when the integrable K-invariant functions on N form a commutative algebra under convolution. We prove that in this case the coadjoint orbits for G := K nN which meet the annihilator k⊥ of the Lie algebra k of K do so in single K-orbits. This generalizes a result of the authors and R....

(c,1,...,1) Polynilpotent Multiplier of some Nilpotent Products of Groups

In this paper we determine the structure of (c,1,...,1) polynilpotent multiplier of certain class of groups. The method is based on the characterizing an explicit structure for the Baer invariant of a free nilpotent group with respect to the variety of polynilpotent groups of class row (c,1,...,1).

The Spherical Transform of a Schwartz Function on the Heisenberg Group

Suppose that K ⊂ U(n) is a compact Lie group acting on the (2n+1)dimensional Heisenberg group Hn. We say that (K,Hn) is a Gelfand pair if the convolution algebra LK(Hn) of integrable K-invariant functions on Hn is commutative. In this case, the Gelfand space ∆(K,Hn) is equipped with the GodementPlancherel measure, and the spherical transform ∧ : LK(Hn)→ L(∆(K,Hn)) is an isometry. The main resul...

On the Nilpotent Multiplier of a Free Product