We prove an explicit formula for the conductor of an irreducible, admissible representation of GL(n, F ) twisted by a character of F× where the field F is local and non-archimedean. The components of our formula are analysed, both explicitly and on average, for application to the analytic study of automorphic forms on GL(n). We also demonstrate that “functoriality preserves depth” for such Rank...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Abstract Kottwitz’s conjecture describes the contribution of a supercuspidal representation to cohomology local Shimura variety in terms Langlands correspondence. A natural extension this concerns Scholze’s more general spaces shtukas. Using new Lefschetz–Verdier trace formula for v-stacks, we prove extended conjecture, disregarding action Weil group, and modulo virtual whose character vanishes...

We consider the category of smooth W (k)[GLn(F )]-modules, where F is a p-adic field and k is an algebraically closed field of characteristic ` different from p. We describe a factorization of this category into blocks, and show that the center of each such block is a reduced, `-torsion free, finite type W (k)-algebra. Moreover, the k-points of the center of a such a block are in bijection with...

Abstract Given a regular supercuspidal representation $$\rho $$ ρ of the Levi subgroup M standard parabolic $$P=MN$$ P = M N in connected reductive group G defined over non-archimedean local field F , we serve you Rodie...

These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...