Related papers: Partial Dirac Cohomology and Tempered Representati…

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the…

Within the group algebras of the symmetric and hyperoctahedral groups, one has their descent algebras and families of Eulerian idempotents. These idempotents are known to generate group representations with topological interpretations, as…

Up to equivalence, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology for the simple Lie group $E_{6(-14)}$, which is of Hermitian symmetric type. Each FS-scattered Dirac series of $E_{6(-14)}$…

A relativistic Hamiltonian mechanical system is seen as a conservative Dirac constraint system on the cotangent bundle of a pseudo-Riemannian manifold. We provide geometric quantization of this cotangent bundle where the quantum constraint…

We explain by elementary means why the existence of a discrete series representation of a real reductive group $G$ implies the existence of a compact Cartan subgroup of $G$. The presented approach has the potential to generalize to real…

In this paper, we extend the work in "Morita's Theory for the Symplectic Groups" to split reductive groups. We construct and study the holomorphic discrete series representation and the principal series representation of a split reductive…

In a previous work (arXiv:0806.1503v2), we defined a family of subcomplexes of the $n$-dimensional half cube by removing the interiors of all half cube shaped faces of dimension at least $k$, and we proved that the homology of such a…

We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. The representation theory of restricted Lie algebras is reviewed including a description of the restricted universal enveloping algebra. In the case of…

In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…

This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…

We survey some of the known results on the relation between the homology of the {\em full} Hecke algebra of a reductive $p$-adic group $G$, and the representation theory of $G$. Let us denote by $\CIc(G)$ the full Hecke algebra of $G$ and…

Let $G$ be a connected semisimple noncompact real Lie group and let $\rho: G \longrightarrow \mathrm{SL}(V)$ be a representation on a finite dimensional vector space $V$ over $\mathbb R$, with $\rho(G)$ closed in $\mathrm{SL}(V)$.…

There is a well-known correspondence between the symplectic variety of representations of the fundamental group of a punctured Riemann surface into a compact Lie group G, with fixed conjugacy classes at the punctures, and a complex variety…

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…

In this paper, we present a unified framework for studying cohomology theories of various operators in the context of pseudoalgebras. The central tool in our approach is the notion of a quasi-twilled Lie pseudoalgebra. We introduce two…

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite…

In this paper we study the problem of computing the Dirac cohomology of the special unipotent representations of the real groups Sp(2n,R) and U(p,q).

We study how the partial group (co)homology of a group $G$ with coefficient in a partial representation $M$ can be described using the usual group (co)homology. To address this, we introduce the concept of the \textit{universal…

Let G be a quasi-split reductive group over a non-archimedean local field. We establish a local Langlands correspondence for all irreducible smooth complex G-representations in the principal series. The parametrization map is injective, and…