Plancherel measures for coverings of p-adic SL2(F)

ASYMPTOTICS OF q-PLANCHEREL MEASURES

In this paper, we are interested in the asymptotic size of the rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order n, so it does not fit in the context of the work of P. Biane and P. Śniady. Using the theory of polynomial functions on Young diagrams of Kerov and Olsha...

p-Adic Measures and Bernoulli Numbers

Asymptotics of Plancherel Measures for Symmetric Groups

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...

Singular p-adic transformations for Bernoulli product measures

Ergodic properties of p-adic transformations have been studied with respect to Haar measure. This paper extends the study of these properties to measures beyond Haar measure. Under these measures, coefficients do not appear in equal proportions. Adding a rational number that is not an integer then takes likely strings of coefficients to one of two unlikely strings of coefficients. It follows fr...

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.