The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known res...

We study asymptotics of reducible representations of symmetric groups Sq for large q. We decompose such a representation as a sum of irreducible components (or, alternatively, Young diagrams) and we ask what is the character of a randomly chosen component (or, what is the shape of a randomly chosen Young diagram). Our main result is that for a large class of representations the fluctuations of ...

Version of 8/13/05 By Jason Fulman University of Pittsburgh Department of Mathematics, 301 Thackeray Hall, Pittsburgh PA 15260 email: [email protected] Abstract: Stein’s method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term...

We study deformations of the Plancherel measure of the symmetric group by lifting them to the symmetric group and using combina-torics of card shuffling. The existing methods for analyzing deformations of Plancherel measure are not obviously applicable to the examples in this paper. The main idea of this paper is to find and analyze a formula for the total variation distance between iterations ...

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product group G = R ⋊ H have been studied by various authors. Recently the attention has shifted from the irreducible case to include more general dilation groups H , for instance cyclic (more generally: discrete) or one-parameter groups. These groups do not give rise to irreducible square-integrable repr...

The aim of this paper is to prove new uncertainty principles for an integral operator T with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function f ∈ L(R, μ) is highly localized near a single point then T (f) cannot be concentrated in a set of finite measure. The second...

We discuss some existence conditions of the Shehu transform, we provide a Plancherel formula and also relate equicontinuity to exponential L2-equivanishing.

We discuss a Plancherel formula for countable groups, which provides canonical decomposition of the regular representation such group Γ into direct integral factor representations. Our main result gives precise description this in terms FC-center Γfc (that is, normal subgroup consisting elements with finite conjugacy class); involves action an appropriate totally disconnected compact automorphi...

We show in this paper that the Plancherel measure of the symmetric group S n converges weakly (as n ! 1) to a Gaussian random process in the innnite dimensional vector space. With respect to the law of large numbers for this group, found earlier in 1,2] this assertion is analogous to the central limit theorem. The idea of such a result was mentioned in 3]. In the course of preparation of the ar...