Related papers: Schwartz correspondence for real motion groups in …

Let $G$ be a reductive group over a local field $F$ of characteristic zero, Archimedean or not. Let $X$ be a $G$-space. In this paper we study the existence of generalized Whittaker quotients for the space of Schwartz functions on $X$,…

In recent work, we related the structure of subvarieties of $n\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\mathbb{C})$-orbits on the flag variety of $\mathfrak{gl}(n,\mathbb{C})$. In the first part of this…

Given a real semisimple connected Lie group $G$ and a discrete subgroup $\Gamma < G$ we prove a precise connection between growth rates of the group $\Gamma$, polyhedral bounds on the joint spectrum of the ring of invariant differential…

Let X be an irreducible reduced complex space on which a connected compact Lie group K acts by holomorphic automorphisms. Let G be the complexification of K and g the Lie algebra of G. Following the theory of algebraic transformation…

We construct a covariant generating function for the spectrum of chiral primaries of symmetric orbifold conformal field theories with N=(4,4) supersymmetry in two dimensions. For seed target spaces K3 and T4, the generating functions…

Let $\mathbb{H}^{n}$ be the $(2n+1)$-dimensional Heisenberg group, and let $K$ be a compact subgroup of U(n), such that $(K,\mathbb{H}^{n})$ is a Gelfand pair. Also assume that the $K$-action on $\mathbb{C}^n$ is polar. We prove a…

For a locally compact group $G$ and compact subgroup $K$, we consider a Delsarte-type extremal problem for $G$-invariant positive definite kernels on the homogeneous space $G/K$, generalising a certain Tur\'an problem for isotropic positive…

We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution $\sigma_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the…

Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair $(S(n)\times S(n),\Diag S(n))$. They form an orthogonal basis in the space of the functions on the group S(n)…

Let $G$ be a Lie group and let $M$ be a proper smooth $G$-manifold. If $M$ is connected and $\dim(M)\geq 2$, the group of diffeomorphisms of $M$, that are isotopic to the identity through a compactly supported isotopy, acts $n$-transitively…

A kind of generalized Gelfand pair is introduced via a Banach algebra consisting of bi-invariant functions in a weighted Lebesgue space. The related spherical functions and the Fourier transformation are constructed. The multipliers of the…

This paper is a follow-up contribution to our work [20] where we discussed some invariant subspace results for contractions on Hilbert spaces. Here we extend the results of [20] to the context of n-tuples of bounded linear operators on…

In this article, using the notion of group contraction, we obtain the spherical functions of the strong Gelfand pair $(\mathrm{M}(n),\mathrm{SO}(n))$ as an appropriate limit of spherical functions of the strong Gelfand pair…

Let $G$ be a compact Lie group. We prove that if $V$ and $W$ are orthogonal $G$-representations such that $V^G=W^G=\{0\}$, then a $G$-equivariant map $S(V) \to S(W)$ exists provided that $\dim V^H \leq \dim W^H$ for any closed subgroup…

Let G/K be an irreducible Hermitian symmetric space and let D be a K-invariant domain in G/K. In this paper we characterize several classes of K-invariant plurisubharmonic functions on D in terms of their restrictions to a slice…

We extend SO(4,2) covariant lightcone embedding methods of four-dimensional CFTs to N=1 superconformal field theory (SCFT). Manifest superconformal SU(2,2|1) invariance is achieved by realizing 4D superconformal space as a surface embedded…

We consider the notion of a confluent spherical function on a connected semisimple Lie group, $G,$ with finite center and of real rank $1,$ and discuss the properties and relationship of its algebra with the well-known Schwartz algebra of…

Let $G$ be a compact subgroup of $GL_n(\R)$ acting linearly on a finite dimensional vector space $E$. B. Malgrange has shown that the space $\mathcal{C}^\infty(\R^n,E)^G$ of $\mathcal{C}^\infty$ and $G$-covariant functions is a finite…

We investigate the structure of the ring ${\mathbb D}_G(X)$ of $G$-invariant differential operators on a reductive spherical homogeneous space $X=G/H$ with an overgroup $\widetilde{G}$. We consider three natural subalgebras of ${\mathbb…