Related papers: Regular irreducible characters of a hyperspecial c…

A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…

In this paper, we will point out a gap in the proof of a theorem of G.Hill (J. Algebra, 174 (1995), 610-635) and will give new arguments to give a remedy in the non-dyadic case modulo a conjecture on the triviality of certain Schur…

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…

We find all irreducible constituents of the Weil representation of a unitary group $U_m(A)$ of rank $m$ associated to a ramified quadratic extension $A$ of a finite, commutative, local and principal ring $R$ of odd characteristic. We show…

We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. These representations proved to be useful for the construction of abelian varieties…

We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from…

Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting irreducibly on $W$. Suppose also that $G$ is a classical group with natural module…

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this paper we deal with chains of normal subgroups $1 \triangleleft G_1 \triangleleft \cdots…

Weil's representation is a basic object in representation theory which plays a crucial role in many places: construction of unitary irreducible representations in the frame of the orbit method, Howe correspondence, Theta series,... The…

Let ${\mathcal O}$ be an involutive discrete valuation ring with residue field of characteristic not 2. Let $A$ be a quotient of ${\mathcal O}$ by a nonzero power of its maximal ideal and let $*$ be the involution that $A$ inherits from…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

The purpose of the present paper is to investigate a hypergroup arising from irreducible characters of a compact group G and a closed subgroup of G with finite index. The convolution of this hypergroup is introduced by inducing irreducible…

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 G be a connected simple adjoint p-adic group not isomorphic to a projective linear group PGL(m,D) of a division algebra D, or an adjoint ramified unitary group of a split hermitian form in 3 variables. We prove that G admits an…

We consider irreducible representations of finite quandles over $\mathbb{C}$. For $Q$ a finite quandle whose inner automorphism group $Inn(Q)$ have trivial Schur multipliers, we prove that the irreducible representations of $Q$ can be…

We find the irreducible decomposition of the Weil representation of the unitary group $\mathrm{U}_{2n}(A)$, where $A$ is a ramified quadratic extension of a finite, commutative, local, principal ideal ring $R$ and the nilpotency degree of…

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform…