Related papers: Representations of finite pattern groups

Let G be a simple, simply-connected algebraic group over the complex numbers with Lie algebra $\mathfrak g$. The main result of this article is a proof that each irreducible representation of the fundamental group of the orbit O through a…

Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…

We give a streamlined proof of ${\mathbb A}^1$-representability for $G$-torsors under "isotropic" reductive groups, extending previous results in this sequence of papers to finite fields. We then analyze a collection of group homomorphisms…

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of…

Let $G$ be a connected reductive group over the complex numbers and let $T\subset G$ be a maximal torus. For any $t\in T$ of finite order and any irreducible representation $V(\lambda)$ of $G$ of highest weight $\lambda$, we determine the…

Let $E/F$ be a quadratic extension of fields, and $G$ a connected quasi-split reductive group over $F$. Let $G^{op}$ be the opposition group obtained by twisting $G$ by the duality involution considered by Prasad. Assume that the field $F$…

Let $K[HK_{\Theta}]$ denote the Hecke-Kiselman algebra of a finite oriented graph $\Theta$ over an algebraically closed field $K$. All irreducible representations, and the corresponding maximal ideals of $K[HK_{\Theta}]$, are characterized…

For a certain class of finite posets, we prove that all their irreducible orthoscalar representations are finite-dimensional and describe those, for which there exist essential (non-degenerate) irreducible orthoscalar representations.

Let $F$ be a non Archimedean local field with odd residual characteristic, and let $K$ be a hyperspecial maximal compact subgroup of the $p$-adic symplectic group $G=\mathrm{Sp}_4(F)$. Let $\mathfrak{s}$ be an inertial class for $G$ in the…

Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely generated left $H$-modules. This enables us to obtain an…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We prove that if $G$ is a finite irreducible solvable subgroup of an orthogonal group $O(V,Q)$ with $\dim V$ odd, then $G$ preserves an orthogonal decomposition of $V$ into $1$-spaces. In particular $G$ is monomial. This generalizes a…

Given an inverse semigroup $G_0$ of bounded type, we show, along with some other assumptions, that if the set of incompressible elements of $G_0$ is finite, then any finitely generated subgroup $G$ of the topological full group…

We show that there exists a family of irreducible representations R_i (of finite groups G_i) such that, for any constant t, the average of R_i over t uniformly random elements g_1, ..., g_t of G_i has operator norm 1 with probability…

In this paper we suppose G is a finite group acting tamely on a regular projective curve X over Z and V is an orthogonal representation of G of dimension 0 and trivial determinant. Our main result determines the sign of the…

Let $G$ be a finite group and $\psi(G)=\sum_{g\in{G}}{o(g)}$. There are some results about the relation between $\psi(G)$ and the structure of $G$. For instance, it is proved that if $G$ is a group of order $n$ and…

Let F be a finite extension of Q_p and let G be a connected reductive group over F. We assume that p is big relatively to G. Let G' be an endoscopic group of G. Following Arthur, we have, roughly speaking, a spectral transfer which, to a…

We prove that the quotient of an irreducible representation of a special unitary group of rank greater than 1 cannot be a smooth manifold.

We consider smooth representations of the unit group $G = \mathcal{A}^{\times}$ of a finite-dimensional split basic algebra $\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely,…