Related papers: Restricting Toral Supercuspidal Representations to…

The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal…

Consider the space B of complex $p\times q$ matrces with norm <1. There exists a standard one-parameter family $S_a$ of unitary representations of the pseudounitary group U(p,q) in the space of holomorphic functions on B (i.e. scalar…

Possible short and semi-short positive energy, unitary representations of the Osp(2N|4) superconformal group in three dimensions are discussed. Corresponding character formulae are obtained, consistent with character formulae for the…

Let $F$ be a non-Archimedean local field, with the ring of integers $\mathfrak{o}_F. Let $G=GL_N(F)$, $K=GL_N(\mathfrak{o}_F)$ and $\pi$ a supercuspidal representation of $G$. We show that there exist a unique irreducible smooth…

Let $G$ be a connected, linear, real reductive Lie group with compact centre. Let $K<G$ be compact. Under a condition on $K$, which holds in particular if $K$ is maximal compact, we give a geometric expression for the multiplicities of the…

We establish lower bounds for the operator norms of the Fourier restriction/extension operators associated to monomial curves with affine arclength measure. Furthermore, we prove that the set of all extremizing sequences of such an operator…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

Let F be the function field of a curve over a p-adic field. Let D/F be a central division algebra of prime exponent $\ell$ which is different from p. Assume that F contains a primitive ${\ell}^2$-th root of unity. Then the group…

In this note we prove a certain multiplicity formula regarding the restriction of an irreducible admissible genuine representation of a 2-fold cover $\widetilde{{\rm GL}}_{2}(E)$ of ${\rm GL}_{2}(E)$ to the 2-fold cover $\widetilde{{\rm…

Let K be a field and G a split connected reductive affine algebraic K-group. Let T be a split maximal torus of G, W its finite Weyl group, and R its root system. After fixing a realization of R in G and choosing a simple system for R, one…

Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…

Motivated by relating the representation theory of the split real and $p$-adic forms of a connected reductive algebraic group $G$, we describe a subset of $2^r$ orbits on the complex flag variety for a certain symmetric subgroup. (Here $r$…

In this paper, we study the restriction of an irreducible unitary representation $\pi$ of the universal covering $\widetilde{Sp}_{2n}(\mb R)$ to a Heisenberg maximal parabolic group $\tilde P$. We prove that if $\pi|_{\tilde P}$ is…

Module is effective representation of ring in Abelian group. Linear map of module over commutative ring is morphism of corresponding representation. This definition is the main subject of the book. To consider this definition from more…

We construct all cuspidal l-modular representations of a unitary group in three variables attached to an unramified extension of local fields of odd residual characteristic p with l\neq p. We describe the l-modular principal series and show…

In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects…

We show that a mod-$\ell$-representation of a p-adic group arising from the analogue of Yu's construction is supercuspidal if and only if it arises from a supercuspidal representation of a finite reductive group. This has been previously…

We study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction. As an application, we obtain in a unified way free field realizations and determinant formulas for all…

In this paper, we continue our study of abstract representations of elementary subgroups of Chevalley groups of rank $\geq 2.$ First, we extend our earlier methods to analyze representations of elementary groups over arbitrary associative…

Quantum toroidal algebras are obtained from quantum affine algebras by a further affinization, and, like the latter, can be used to construct integrable systems. These algebras also describe the symmetries of instanton partition functions…