Related papers: Bessel Models for General Admissible Induced Repre…
In the archimedean case, we prove uniqueness of Bessel models for general linear groups, unitary groups and orthogonal groups.
We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets…
In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated…
In this paper we study a generalization of the Jacquet module of a parabolic induction and construct a filtration on it. The successive quotient of the filtration is written by using the twisting functor.
We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…
There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on…
A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the Sklyanin bracket. Using different representations of the…
Given a representation of a unimodular locally compact group, we discuss criteria for associated coherent state expansions in terms of the commuting algebra. It turns out that for those representations that admit such expansions there…
We study the character theory of metabelian and polycyclic groups. It is used to investigate Hilbert-Schmidt stability via the character-theoretic criterion of Hadwin and Shulman. There is a close connection between stability and dynamics…
This article proves a formula relating the multiplicity of an induced representation and that of the inducing datum for the Bessel and the Fourier-Jacobi models over Archimedean local fields by generalizing the approach of C. Moeglin and…
In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.
This article gives conceptual statements and proofs relating parabolic induction and Jacquet functors on split reductive groups over a non-Archimedean local field to the associated Iwahori-Hecke algebra as tensoring from and restricting to…
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…
We give precise conditions under which irreducible representations associated to stability groups induce to irreducible representations for Fell bundle C*-algebras. This result generalizes an earlier result of Echterhoff and the second…
Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of…
A parabolic subalgebra $\mathfrak{p}$ of a complex semisimple Lie algebra $\mathfrak{g}$ is called a parabolic subalgebra of abelian type if its nilpotent radical is abelian. In this paper, we provide a complete characterization of the…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
We prove uniqueness and give precise criteria for existence of split and non-split Bessel models for a class of lowest and highest weight representations of the groups GSp(4,R) and Sp(4,R) including all holomorphic and anti-holomorphic…
In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integers, and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on…
In this note, a general version of Bessel multipliers in Hilbert $C^*$-modules is presented and then, many results obtained for multipliers are extended. Also the conditions for invertibility of generalized multipliers are investigated in…