相关论文: Irreducible Representations of Braid Groups of cor…

Every irreducible component of the variety of semi-simple n-dimensional representations of the modular group has a Zariski dense subset contained in the image of an etale map from a rational quotient variety of representations of a fixed…

We study the $n$th degree representations $\hat{\rho_G}$ of $Cb_{n}$ and $\hat{\rho_B}$ of $C_{n}$, defined by Valerij G. Bardakov, where $Cb_{n}$ is the group of basis conjugating automorphisms and $C_n$ is the group of conjugating…

Let $U_n(q)$ be the upper triangular group of degree $n$ over the finite field $\F_q$ with $q$ elements. In this paper, we present constructions of large degree ordinary irreducible representations of $U_n(q)$ where $n\geq 7$, and then…

If $G$ is a second countable locally compact Hausdorff groupoid with Haar system, we show that every representation induced from an irreducible representation of a stability group is irreducible.

We give a complete classification of simple representations of the braid group B_3 with dimension $\leq 5$ over any algebraically closed f ield. In particular, we prove that a simple d-dimensional representation $\rho: B_3 \to GL(V)$ is…

For every $n\geq 1$, the flat braid group $\mathrm{FB}_n$ is an analogue of the braid group $B_n$ that can be described as the fundamental group of the configuration space $$\left\{ \{x_1, \ldots, x_n \} \in \mathbb{R}^n / \mathrm{Sym}(n)…

This paper and its sequel describe the irreducible representations of the rational Cherednik algebra $H_c(W)$ for a finite Coxeter group $W$ of type $H_4$, $F_4$ with equal parameters, $E_6$, $E_7$, and $E_8$, when $c$ is not a…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…

Let $A$ and $A'$ be two Artin groups of spherical type, and let $A_1,\dots,A_p$ (resp. $A'_1,\dots,A'_q$) be the irreducible components of $A$ (resp. $A'$). We show that $A$ and $A'$ are commensurable if and only if $p=q$ and, up to…

We consider Albeverio- Rabanovich linear representation $\pi$ of the braid group $B_3$. After specializing the indeterminates used in defining the representation to non-zero complex numbers, we prove that the restriction of $\pi$ to the…

Let X be a 2-sphere with n punctures. We classify all conjugacy classes of Zariski-dense representations $$\rho: \pi_1(X)\to SL_2(\mathbb{C})$$ with finite orbit under the mapping class group of X, such that the local monodromy at one or…

In this note, we study irreducible unitary representations of special linear groups of lower ranks, in terms of the matrix models of Gelfand-Naimark and Gelfand-Graev. Review of existing literature is provided. We also add some new…

In this paper we completely classify irreducible tensor products of covering groups of symmetric and alternating groups in characteristic $\not=2$.

This work presents an approach towards the representation theory of the braid groups $B_n$. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids,…

An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power…

Let $F$ be a $p$-adic field. Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the groups $\{GL_n(F)\}_{n=0}^\infty$ taken together, with multiplication defined in the sense of parabolic…

We study Hodge representations of absolutely simple Q-algebraic groups with Hodge numbers h = (1,1,...,1). For those groups that are not of type A, we give a classification of the R-irreducible representations; a similar classification for…

Given a group $G$ and an integer $n\geq 0$ we consider the family $\mathcal{F}_n$ of all virtually abelian subgroups of $G$ of rank at most $n$. In this article we prove that for each $n\ge2$ the Bredon cohomology, with respect to the…

We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or…

The braid groups B_n can be defined as the mapping class group of the n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is the induced action on a certain twisted second homology of the space of unordered pairs of…