Related papers: Bessel Models for General Admissible Induced Repre…
We introduce the notion of a generalized spin representation of the maximal compact subalgebra of a symmetrizable Kac-Moody algebra in order to show that, if defined over a formally real field, every such subalgebra has a non-trivial…
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
In this paper, new integral representations for the Bessel $J$ and $I$ functions were presented and their results were used to derive an expression for the Modified Bessel $K$ function.
In the context of Hecke algebras of complex reflection groups, we prove that the generalized Hecke algebras of normalizers of parabolic subgroups are semidirect products, under suitable conditions on the parameters involved in their…
The relative trace formula of Jacquet-Rallis (for unitary groups or general linear groups) is an identity between periods of automorphic representations and geometric distributions. In this paper, we prove the transfer between all geometric…
In this article we study atomic and molecular decompositions in $2$-microlocal Besov and Triebel--Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the…
Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the existence of a cocompact model of classifying space for proper…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
We study compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces with variable exponents on both bounded and unbounded metric measure spaces. We establish sufficient conditions for compactness, and under additional assumptions, we…
Let G be a finite solvable permutation group. Then modulo a possibly trivial normal elementary abelian 3-subgroup, some set-stabilizer in G is a 2-group.
Let B be the generalized braid group associated to some finite complex reflection group. We define a representation of B of dimension the number of reflections of the corresponding reflection group, which generalizes the Krammer…
We generalize Koll\'ar's package (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles twisted by a multiplier ideal sheaf associated with an…
Emerton's theory of Jacquet modules for locally analytic representations provides necessary conditions for the existence of integral structures in locally analytic representations. These conditions are also expected to be sufficient for the…
We derive an integral representation for the Jacobi-Poisson kernel valid for all admissible type parameters $\alpha,\beta$ in the context of Jacobi expansions. This enables us to develop a technique for proving standard estimates in the…
We study the homomorphisms between scalar generalized Verma modules. We conjecture that any homomorphism between is composition of elementary homomorphisms. The purpose of this article is to show the conjecture is affirmative for many…
We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general context of quasi-metric-measure spaces. Although stated in the…
We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…
For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…
Let F be a locally compact non-archimedean field, p its residue characteristic, and G a connected reductive group over F. Let C an algebraically closed field of characteristic p. We give a complete classification of irreducible admissible…