Let H′ (R) denote the set of Associated Homogeneous Distributions (AHDs) with support in R. The set H′ (R) consists of the distributional analogues of one-dimensional power-log functions. H′ (R) is an important subset of the tempered distributions S′ (R), because (i) it contains the majority of the (one-dimensional) distributions typically encountered in physics applications and (ii) recent wor...

Ginzburg and Nakajima have given two different geometric constructions of quotients of the universal enveloping algebra of sln and its irre-ducible finite-dimensional highest weight representations using the convolution product in the Borel-Moore homology of flag varieties and quiver varieties respectively. The purpose of this paper is to explain the precise relationship between the two constru...

Let K be a compact Lie group acting on a finite dimensional Hermitian vector space V via some unitary representation. Now K acts by automorphisms on the associated Heisenberg group HV = V × R and we say that (K,HV ) is a Gelfand pair when the algebra LK(HV ) of integrable K-invariant functions on HV commutes under convolution. In this situation an application of the Orbit Method yields a inject...

In this paper, we treat some fractional differential equations on the sequence Lebesgue spaces ℓp(N0) with p≥1. The Caputo calculus extends usual derivation. operator, associated to Cauchy problem, is defined by a convolution of compact support and belongs Banach algebra ℓ1(Z). We in detail these sequences. use techniques from algebras Functional Analysis explicity check solution problem.

Let $G$ be a split connected reductive group over finite field of characteristic $p > 2$ such that $G_\text{der}$ is absolutely almost simple. We give geometric construction perverse $\mathbb{F}_p$-sheaves on the Iwahori affine flag variety which are central with respect to convolution product. deduce an explicit formula for isomorphism from spherical mod $p$ Hecke algebra center algebra. also ...

1.1. Let G be an almost simple complex algebraic group, and let GrG be its affine Grassmannian. Recall that if we set O = C[[t]], F = C((t)), then GrG = G(F)/G(O). It is well-known that the subgroup ΩK of polynomial loops into a maximal compact subgroup K ⊂ G projects isomorphically to GrG; thus GrG acquires the structure of a topological group. An algebro-geometric counterpart of this structur...