Related papers: Two geometric character formulas for reductive Lie…

Let $V$ be a finite abelian group of odd order, equipped with a non-degenerate, alternating form $\omega\colon V\times V \to \mathbb{Z}/m\mathbb{Z}$. We give closed formulas for the character values of the Weil representation associated…

For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the…

In this paper we are mainly concerned with the study of polarizations (in general of higher-order type) on a connected Lie group with a U(1)-principal bundle structure. The representation technique used here is formulated on the basis of a…

Anosov representations give a higher-rank analogue of convex cocompactness in a rank-one Lie group which shares many of its good geometric and dynamical properties; geometric finiteness in rank one may be seen as a controlled weakening of…

We provide characterizations of Anosov representations of word hyperbolic groups into real semisimple Lie groups in terms of the existence of equivariant limit maps on the Gromov boundary, the Cartan property and the uniform gap summation…

Let $\mathcal{O}_2$ and $\mathcal{O}'_2$ be two distinct finite local rings of length two with residue field of characteristic $p$. Let $\mathbb{G}(\mathcal{O}_2)$ and $\mathbb{G}(\mathcal{O}'_2)$, be the group of points of any reductive…

Using method of inducing, irreducible unitary representation of Cayley--Klein orthogonal groups were constructed. There was proved that Kirilov's method of orbits is relevant for study of the behavior of irreducible representations under…

In this paper we provide a geometric framework for the study of characters of depth-zero representations of unramified groups over local fields with finite residue fields which is built directly on Lusztig's theory of character sheaves for…

Vogan and Barbasch-Vogan attach two similar invariants to representations of a reductive Lie group, one by an algebraic process, the other analytic. They conjectured that the two invariants determine each other in a definite manner. Here we…

In this work, we generalize the notion of character for 2-representations of finite 2-groups. The properties of 2-characters bear strong similarities to those classical characters of finite groups, including conjugation invariance,…

We develop general formulae for the numbers of conjugacy classes and irreducible complex characters of finite p-groups of nilpotency class less than p. This allows us to unify and generalize a number of existing enumerative results, and to…

This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent…

Let $G$ be a simply connected nilpotent Lie group with Lie algebra $\frak g$; let $\frak g^*$ be the dual of $\frak g$. Let $\Omega$ be a locally compact second countable Hausdorff space with a continuous $G$ action, and let $C^*(G,\Omega)$…

The Iwahori--Hecke and Yokonuma--Hecke algebras have played crucial roles in algebraic combinatorics and the representation theory of finite groups. In this work, we use classical results from representation theory to compute the character…

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.

We describe the resolution of field identification fixed points in coset conformal field theories in terms of representation spaces of the coset chiral algebra. A necessary ingredient from the representation theory of Kac Moody algebras is…

We prove that the action of a reductive complex Lie group on a K\"ahler manifold can be linearized in the neighbourhood of a fixed point, provided that the restriction of the action to some compact real form of the group is Hamiltonian with…

Let $\Gamma$ be a finitely generated nilpotent group and let G be a complex reductive algebraic group. The representation variety $\mathrm{Hom}(\Gamma,G)$ and the character variety $\mathrm{Hom}(\Gamma,G)//G$ each carry a natural topology,…

We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…