相关论文: Integrability and singularities of Harish-Chandra …

In this paper under some conditions we generalize a theorem of Harish-Chandra concerning representability of Fourier transforms of orbital integrals.

Let $M$ be a $3$-manifold, compact with boundary and $\Gamma$ its fundamental group. Consider a complex reductive algebraic group G. The character variety $X(\Gamma,G)$ is the GIT quotient $\mathrm{Hom}(\Gamma,G)//G$ of the space of…

Let $L(\lambda)$ be a highest weight Harish-Chandra module with highest weight $\lambda$. When the associated variety of $L(\lambda)$ is not maximal, that is, not equal to the nilradical of the corresponding parabolic subalgebra, we prove…

We consider a classical Hamiltonian $H$ on $\mathbb{R}^{2d}$, invariant by a finite group of symmetry $G$, whose Weyl quantization $\hat{H}$ is a selfadjoint operator on $L^2(\mathbb{R}^d)$. If $\chi$ is an irreducible character of $G$, we…

Let F be a non-archimedean local field, of characteristic 0. Let V be a finite dimensional vector space over F and q be a non-degenerate quadratic form on V. Denote d the dimension of V and G=SO(d) the special orthogonal group of (V,q). Let…

Let $G$ be a connected reductive $p$-adic group and let $\theta$ be an automorphism of $G$ of order at most two. Suppose $\pi$ is an irreducible smooth representation of $G$ that is taken to its dual by $\theta$. The space $V$ of $\pi$ then…

We introduce reflection properties of cardinals in which the attributes that reflect are expressible by infinitary formulas whose lengths can be strictly larger than the cardinal under consideration. This kind of generalized reflection…

Characteristic cycles and leading term cycles of irreducible highest weight Harish-Chandra modules of regular integral infinitesimal character are determined. In the simply laced cases they are irreducible, but in the nonsimply laced cases…

For a connected quasi-split reductive algebraic group $G$ over a field $k$, which is either a finite field or a non-archimedean local field, $\theta$ an involutive automorphism of $G$ over $k$, let $K =G^\theta$. Let $K^1=[K^0,K^0]$, the…

We consider the 2-D incompressible Euler equations in a bounded domain and show that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity…

Let $F$ be a $p$-adic field, $G = \text{GL}_{2n}(F)$ and $\theta_0$ be the exterior automorphism of $G$ that fixes a pinning of a Borel pair. Consider the set $\widetilde{G} = G \theta_0$ on which $G$ acts by conjugacy and the orbital…

Let $G$ be a reductive Lie group and ${\mathcal O}$ the coadjoint orbit of a hyperbolic element of ${\frak g}^*$. By $\pi$ is denoted the unitary irreducible representation of $G$ associated with ${\mathcal O}$ by the orbit method. We give…

Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $\sigma$ be an involution of the…

Using hyperbolic localization, we identify the nearby cycles along the Vinberg degeneration with the composition of Radon and Harish-Chandra functors, both considered for the category of character sheaves. This provides a new, simple proof…

This paper contains a non-trivial generalization of the Harish-Chandra transforms on a connected semisimple Lie group $G,$ with finite center, into what we term spherical convolutions. Among other results we show that its integral over the…

Let G be the group GL(N,F), where F is a non-archimedean locally compact field. Using Bushnell and Kutzko's simple types, as well as an original idea of Henniart's, we construct explicit pseudo-coefficients for the discrete series…

In this paper we study singular integral operators which are hyper or weak over Lipschitz or Holder spaces and over weghted Sobolev spaces defined on unbounded domains in the standard $n$-D space $R^n$ for $n>0$. The $\pi$-operator in this…

We prove that the Hilbert scheme of the plane in positive characteristic admits an invertible top differential form. This implies certain integrability properties of the symmetric powers of the plane. This allows to define a function on the…

Let $G$ be a finite group and $p\in \pi(G)$, and let Irr$(G)$ be the set of all irreducible complex characters of $G$. Let $\chi \in {\rm Irr}(G)$, we write ${\rm cod}(\chi)=|G:{\rm ker} \chi|/\chi(1)$, and called it the codegree of the…

Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse…