Related papers: Dirac cohomology and unipotent representations of …

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

We study unitary representations associated to cocycles of measurable dynamical systems. Our main result establishes conditions on a cocycle, ensuring that ergodicity of the dynamical system under consideration is equivalent to…

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

Let $G$ be $Sp(2n, \mathbb{R})$ or $SO^*(2n)$. We compute the Dirac index of a large class of unitary representations considered by Vogan in Section 8 of [Vog84], which include all weakly fair $A_{\mathfrak{q}}(\lambda)$ modules and…

The Dirac monopole problem is studied in details within the framework of infinite-dimensional representations of the rotation group, and a consistent pointlike monopole theory with an arbitrary magnetic charge is deduced.

We generalize a cohomological construction of representations due to Lusztig from the hyperspecial case to arbitrary parahoric subgroups of a reductive group over a local field, which splits over an unramified extension. We compute the…

For an arbitrary unimodular Lie group $G$, we construct strongly continuous unitary representations in the Bergman space of a naturally constructed strongly pseudoconvex neighborhood of $G$ in the complexification of its underlying…

Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…

Some question about representations of $p$-adic groups are discussed.

We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…

We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…

We study the action of the dihedral group on the (equivariant) cohomology of the toric manifolds associated with cycle graphs.

Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincar\'e…

Up to equivalence, this paper classifies all the irreducible unitary representations with non-zero Dirac cohomology for the following simple real exceptional Lie groups: ${\rm EI}=E_{6(6)}, {\rm EIV}=E_{6(-26)}, {\rm FI}=F_{4(4)}, {\rm…

I present several applications of the Dirac inequality to the determination of isolated unitary representations and associated "spectral gaps" in the case of unramified principal series. The method works particularly well in order to attach…

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

The smooth hermitian representations of a split reductive p-adic group whose restriction to a maximal hyperspecial compact subgroup contain a single K-type with Iwahori fixed vectors have been studied in [D. Barbasch, A. Moy, Classification…

In this paper, we study Lie-Rinehart cohomology for quotients of singularities by finite groups, and interpret these cohomology groups in terms of integrable connection on modules.

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…

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…