Related papers: On the sign representations for the complex reflec…

We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We…

Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation between three types of representations of G: positive energy (unitary lowest weight)representations,…

Iwahori-Hecke algebras for the infinite series of complex reflection groups $G(r,p,n)$ were constructed recently in the work of Ariki and Koike, Brou\'e and Malle, and Ariki. In this paper we give Murnaghan-Nakayama type formulas for…

Let $r$ be a positive integer and let $G_n$ be the reflection group of $n \times n$ monomial matrices whose entries are $r^{th}$ complex roots of unity and let $k \leq n$. We define and study two new graded quotients $R_{n,k}$ and $S_{n,k}$…

A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.

In this paper, we describe the irreducible representations in category O of the rational Cherednik algebra H_c(G_12,h) associated to the complex reflection group G_12 with reflection representation h for an arbitary complex parameter c. In…

We give combinatorial models for complex, smooth, non-spherical, generic, irreducible representations of the group G=PGL(2,F), where F is a non-archimedean locally compact field. They use the graphs X_k lying above the tree of G, introduced…

Let $\rho : \Gamma \longrightarrow G$ be a Zariski dense irreducible convex representation of the hyperbolic group $\Gamma$, where G is a connected real semisimple algebraic Lie group. We establish a central limit type theorem for the…

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such…

In this paper, we construct a mixed-base number system over the generalized symmetric group $G(m,1,n)$, which is a complex reflection group with a root system of type $B_n^{(m)}$. We also establish one-to-one correspondence between all…

Let $G$ be a real compact Lie group, such that $G=G^0\rtimes C_2$, with $G^0$ simple. Here $G^0$ is the connected component of $G$ containing the identity and $C_2$ is the cyclic group of order $2$. We give a criterion for whether an…

We investigate the representation of a symmetric group $S_n$ on the homology of its Quillen complex at a prime $p$. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

For a semisimple, simply-connected linear algebraic group, $G$, and parabolic subgroup, $P\subseteq G$, we use the fact that the Hilbert polynomial of the equivariant embedding of $G/P$ is equal to the Hilbert function to compute an…

In this article we describe the 2-cocycles, Schur multiplier and representation group of discrete Heisenberg groups over the unital rings of order $p^2$. We describe all projective representations of Heisenberg groups with entries from the…

Let $G$ be a $p$-adic classical group. The representations in a given Bernstein component can be viewed as modules for the corresponding Hecke algebra---the endomorphism algebra of a pro-generator of the given component. Using Heiermann's…

In this paper, we prove the Regev formulae for the characters of the Ariki--Koike algebras by applying the Schur--Sergeev reciprocity between the quantum superalgebras and the Ariki--Koike algebras, which is a generalization of the formulas…

We introduce the Pythagorean C*-algebras and use the category/functor method to construct unitary representations of Thompson's groups from representations of them. We calculate several examples.

Let $G$ be a finite group, and let $\mathbf{K}_p$ denote the completion at $p$ of the complex $K$-theory spectrum. $\mathbf{K}_p$ is a commutative ring spectrum that in some ways is very similar to the usual ring $\mathbf{Z}_p$ of $p$-adic…