Related papers: Exceptional supercuspidal representations in small…

In this paper, we compute the characters of the simple supercuspidal representations of SL(2,F) and SL(3,F) on split tori. Here, F is an arbitrary non-Archimedean local field of characteristic zero.

We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…

Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in…

This article has a twofold purpose. First, by recent works of Kaletha and Loke-Ma, we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic-orthogonal case.…

Let $F$ be a non-archimedean local field with odd residual characteristic, and let $H$ be a maximal torus of ${\rm GL}_2(F)$. In this paper, we will classify the irreducible $H$-distinguished representations of ${\rm GL}_2(F)$ by using…

The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…

We classify the unitary representations of the extended Poincar\'e supergroups in three dimensions. Irreducible unitary representations of any spin can appear, which correspond to supersymmetric anyons. Our results also show that all…

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

We introduce a new integral representation for the standard L-function of an irreducible cuspidal automorphic representation of the exceptional group G2, and also for the twist of this L-function by an arbitrary character. Because our…

Let $G$ be an inner form of a general linear group or classical group over a non-archimedean local field of residual characteristic $p$, assumed odd in the classical case. We prove that every smooth representation of $G$ over an…

Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an…

All unitary irreducible representations of centrally extended (N-odd) N-conformal Galilei group are constructed. The "on-shell" action of the group is derived and shown to coincide, in special but most important case, with that obtained in:…

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…

Using methods from the theory of residue currents we provide asymptotic expansions of certain divergent integrals on complex manifolds. We express the coefficients in these expansions with the conjugate Dolbeault residue, introduced by…

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…

We obtain an upper bound for the dimension of the cuspidal automorphic forms for $\mathrm{GL}_2$ over a number field, whose archimedean local representations are not tempered. More precisely, we prove the following result. Let $F$ be a…

Let G be a connected split adjoint semi simple p-adic Lie group. This paper can be seen as a continuation of [12] and is about the construction of locally analytic G-representations which do not lie in the principal series. Here we consider…

In this paper we consider the representation theory of N=1 Super-W-algebras with two generators for conformal dimension of the additional superprimary field between two and six. In the superminimal case our results coincide with the…

We study the Weil representation $\rho$ of a curve over a $p$-adic field with potential reduction of compact type. We show that $\rho$ can be reconstructed from its stable reduction. For superelliptic curves of the form $y^n=f(x)$ at primes…

Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…