相关论文: Whittaker normalization of $p$-adic ABV-packets an…

We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…

We consider the adiabatic regime of two parameters evolution semigroups generated by linear operators that are analytic in time and satisfy the following gap condition for all times: the spectrum of the generator consists in finitely many…

It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their…

The package performs molecular-dynamics-like agent-based simulations for models of aligning self-propelled particles in two dimensions such as e.g. the seminal Vicsek model or variants of it. In one class of the covered models, the…

We consider the restriction and induction of representations between a covering group and its derived subgroup, both on the representation-theoretic side and the L-parameter side. In particular, restriction of a genuine principal series is…

Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the…

In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…

We study the structures of Fourier coefficients of automorphic forms on symplectic groups based on their local and global structures related to Arthur parameters. This is a first step towards the general conjecture on the relation between…

We construct wave packets for the hydrogen atom labelled by the classical action-angle variables with the following properties. i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable…

This thesis deals with deformations of VB-algebroids and VB-groupoids. They can be considered as vector bundles in the categories of Lie algebroids and groupoids and encompass several classical objects, including Lie algebra and Lie group…

This paper studies the algebraic aspect of a general abelian coset theory with a work of Dong and Lepowsky as our main motivation. It is proved that the vacuum space $\Omega_{V}$ (or the space of highest weight vectors) of a Heisenberg…

We develop a detailed arithmetic theory related to special values at arbitrary integers of the Artin $L$-series of linear characters. To do so we define canonical generalized Stark elements of arbitrary `rank' and `weight', thereby…

Suppose a finite dimensional semisimple Lie algebra $\mathfrak g$ acts by derivations on a finite dimensional associative or Lie algebra $A$ over a field of characteristic $0$. We prove the $\mathfrak g$-invariant analogs of Wedderburn -…

Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…

Let $\pi $ be an irreducible smooth complex representation of a general linear $p$-adic group and let $\sigma $ be an irreducible complex supercuspidal representation of a classical $p$-adic group of a given type, so that $\pi\otimes\sigma…

This article is on the parametrization of the local Langlands correspondence over local fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set…

We prove a combinatorial rule for a complete decomposition, in terms of Langlands parameters, for representations of p-adic $GL_n$ that appear as parabolic induction from a large family (ladder representations). Our rule obviates the need…

We demonstrate that the application of any external uniform non-abelian gauge background, no matter how small, leads to a greatly enhanced degeneracy. This degeneracy is so large that even a non-abelian background field of infinitesimal…

Let $\pi, \pi'$ be irreducible tempered representations of an affine Hecke algebra H with positive parameters. We compute the higher extension groups $Ext_H^n (\pi,\pi')$ explicitly in terms of the representations of analytic R-groups…

We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on…