Related papers: Notes on unitary theta representations of compact …

We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an…

We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a…

This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations

I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.

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.

Restriction of functions from a reductive p-adic group G to its compact subgroups defines an operator on the Hochschild and cyclic homology of the Hecke algebra of G. We study the commutation relations between this operator and others…

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as…

This is a list of questions raised by our joint work arXiv:1412.0737 and its sequels.

We initiate the systematic study of modular representations of symmetric groups that arise via the braiding in (symmetric) tensor categories over fields of positive characteristic. We determine what representations appear for certain…

Harmonic functions of the three dimensional Lie groups defined on certain manifolds related to the Lie groups themselves and carrying all their unitary representations are explicitly constructed. The realisations of these Lie groups are…

We survey some recent advances in the homotopy theory of classifying spaces, and homotopical group theory. We focus on the classification of p-compact groups in terms of root data over the p-adic integers, and discuss some of its…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

Using the Kirillov orbit method, novel methods from p-adic integration and Clifford theory, we study representation zeta functions associated to compact p-adic analytic groups. In particular, we give general estimates for the abscissae of…

We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.

In this paper, we completely describe the Howe correspondence for the dual pairs from the title over a nonarchimedean local field of characteristic zero. More specifically, for every irreducible admissible representation of these groups, we…

The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…

In this paper, we construct certain unipotent representations for the real orthogonal group and the metaplectic group in the sense of Vogan. Our construction is based on quantum induction which involves the compositions of even number of…

We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us to establish that the representation zeta functions of…