Related papers: Restricting Toral Supercuspidal Representations to…

For any representation of a complex simple Lie algebra $\mathfrak{sl}_n$, one problem of branching rules to $\mathfrak{sl}_2$-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion…

We consider spherical principal series representations of the semisimple Lie group of rank one $G=SO(n, 1; \mathbb K)$, $\mathbb K=\br, \bc, \bh$. There is a family of unitarizable representations $\pi_{\nu}$ of $G$ for $\nu$ in an interval…

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…

Suppose that $H$ is a closed subgroup of a locally compact group $G$. We show that a unitary representation $U$ of $H$ is the restriction of a unitary representation of $G$ if and only if a dual representation $\hat U$ of a crossed product…

Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex…

We give an explanation of the bijection between geometric and arithmetic diagrams attached to supercuspidal unipotent representations of a simple p-adic group which is based purely on algebra. The second version contains much additional…

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U_q[osp(1/2)] and the corresponding supergroup OSp_q(1/2). The classical q-->1 limit of this universal T-matrix yields the…

In this article we revisit some classical conjectures in harmonic analysis in the setting of mixed norm spaces $L^p_{rad} L^2_{ang} (\mathbb{R}^n)$. We produce sharp bounds for the restriction of the Fourier transform to compact…

We generalize the concept of cubic group into any dimension and derive their conjugate classifications and representation theorys. Double group and spinor representation are defined. A detailed calculation is carried out on the structures…

This paper studies the behavior of Jiu-Kang Yu's tame supercuspidal representations relative to involutions of reductive p-adic groups. Symmetric space methods are used to illuminate various aspects of Yu's construction. Necessary…

We wish to understand how irreducible representations of a group G behave when restricted to a subgroup G' (the branching problem). Our primary concern is with representations of reductive Lie groups, which involve both algebraic and…

In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms appearing in the results of D'Hoker and…

Quasirational presentations ($QR$-presentations) of (pro-$p$)groups are studied. Such presentations include, in particular, aspherical presentations of discrete groups and their subpresentations and pro-$p$-groups with a single defining…

We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…

We study finite-rank left-translation invariant algebraic $D$-modules on complex affine algebraic groups. Using the standard description of these objects as left-invariant flat algebraic connections on the trivial vector bundle, modulo…

Let F be a non-archimedean local field of odd residual characteristic. Let G be a (connected) reductive group over F that splits over a tamely ramified field extension of F. We revisit Yu's construction of smooth complex representations of…

We obtain a realization of the Lie superalgebra $D(2, 1 ; \alpha)$ in differential operators on the supercircle $S^{1|2}$ and in $4\times 4$ matrices over a Weyl algebra. A contraction of $D(2, 1 ; \alpha)$ is isomorphic to the universal…

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is…

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…

We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…