Related papers: Representability of $GL_E$

Let $V$ denote a vector space over two-element field $\mathbb F_2$ with finite positive dimension and endowed with a symplectic form $B.$ Let ${\rm SL}(V)$ denote the special linear group of $V.$ Let $S$ denote a subset of $V.$ Define…

We show that the category of V-groups, where V is a cartesian quantale, so in particular the category of preordered groups, is locally algebraically cartesian closed with respect to the class of points underlying the product V-category…

Let G be a connected reductive group defined over a finite field F_q. We give a parametrization of the irreducible representations of G(F_q) in terms of (twisted) categorical centres of various monoidal categories associated to G. (Results…

Let $\mathbb{F}$ be a non-archimedean local field of positive characteristic different from 2. We consider distributions on $\mathrm{GL}(n+1,\mathbb{F})$ which are invariant under the adjoint action of $\mathrm{GL}(n,\mathbb{F})$. We prove…

Let $G$ be a complex reductive group. The spherical Hecke category of $G$ can be presented as the category of $G_{\mathcal O}$-equivariant constructible sheaves on the affine Grassmannian $\mathrm{Gr}_G$. This category admits a convolution…

We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in existence…

Let $G=Sp(4,\mathbb{R})$ and let $\pi$ be an irreducible, unitary representation of $G$ which is cohomological with respect to trivial coefficients. Using the inclusion from $SO(5,\mathbb{C})$ to $GL(5,\mathbb{C})$, we transfer $\pi$ to an…

In this paper, we describe Galois covers of algebraic curves and their families by using local systems associated to push-forward of sheaves by the structure morphism. More precisely, if $f:C\to Y$, we consider the sheaves $f_*(\C)$. The…

We prove that the additive group $(E^\ast,\tau_k(E))$ of an $\mathscr{L}_\infty$-Banach space $E$, with the topology $\tau_k(E)$ of uniform convergence on compact subsets of $E$, is topologically isomorphic to a subgroup of the unitary…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

This paper develops various foundational results in the locally analytic representation theory of p-adic groups. In particular, we define the functor ``pass to locally analytic vectors'', which attaches to any continuous representation of a…

Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that picks…

Let $SL_{2}(F_{q})$ be the special linear group over a finite field $F_{q}$, $V$ be the 2-dimensional natural representation of $SL_{2}(F_{q})$ and $V^{\ast}$ be the dual representation. We denote by $F_{q}[V\oplus…

Let K be any field, and let G be a semisimple group over K. Suppose the characteristic of K is positive and is very good for G. We describe all group scheme homomorphisms phi:SL(2) --> G whose image is geometrically G-completely reducible…

In this work, we study multiplicity-free induced representations of finite groups. We analyze in great detail the structure of the Hecke algebra corresponding to the commutant of an induced representation and then specialize to the…

Let G be an infinitesimal group scheme of finite height r and V(G) the scheme which represents 1-parameter subgroups of G. We consider sheaves over the projectivization P(G) of V(G) constructed from a G-module M. We show that if P(G) is…

Each rule $f$ that assigns a vector $f(G)$ to an $(n+1)$-graph $G$ determines a class (or property) of $n$-manifold invariants. An invariant $v=v(M)$ is in this class if, for any triangulated manifold $|G|=M$, one has that $v(M)$ is a…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

This paper is a comprehensive study of the nest representations for the free semigroupoid algebra $\flgee$ of countable directed graph $G$ as well as its norm-closed counterpart, the tensor algebra $\T^{+}(G)$. We prove that the finite…

Let $G$ be a $\mathbb{Q}_p$-split reductive group with connected centre and Borel subgroup $B=TN$. We construct a right exact functor $D^\vee_\Delta$ from the category of smooth modulo $p^n$ representations of $B$ to the category of…