Related papers: Ellipticity and discrete series

In this note we give a self-contained proof of the following classification (up to conjugation) of subgroups of the general symplectic group of dimension n over a finite field of characteristic l, for l at least 5, which can be derived from…

Let $G$ be a reductive $p$-adic group. We give a short proof of the fact that $G$ always admits supercuspidal complex representations. This result has already been established by A. Kret using the Deligne-Lusztig theory of representations…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

A consequence of Rapinchuk et al. is that for $S$ a closed surface of genus $g\geq 2$, the set of Hitchin representations of $\pi_1(S)$ with image in $\mathrm{SL}(n,\mathbb{Q})$ is dense in the Hitchin component. We give a dynamical proof…

Let $\mathcal{G}$ be a quasi-split connected reductive group over a non-archimedean local field $F.$ In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of…

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G X) < dim G for some definable X subset of G then X contains a torsion point of G. Along the way we develop a general theory for…

We prove that any reductive group G over a non-Archimedean local field has a cuspidal complex representation.

Let $G$ be a reductive complex Lie group with Lie algebra $\mathfrak{g}$ and suppose that $V$ is a polar $G$-representation. We prove the existence of a radial parts map $\mathrm{rad}: \mathcal{D}(V)^G\to A_{\kappa}$ from the $G$-invariant…

Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whose nilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We study the degenerate principal series representations of $G$ on $C^\infty(X)$ in the case…

In this article we consider the connected component of the identity of $G$-character varieties of compact Riemann surfaces of genus $g > 0$, for connected complex reductive groups $G$ of type $A$ (e.g., $SL_n$ and $GL_n$). We show that…

We propose a geometrical interpretation for the discrete torsion appearing in the algebraic formulation of quotients of WZW models by discrete abelian subgroups. Part of the discrete torsion corresponds to the choice of action of the…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

We show that a regular locally compact quantum group $\mathbb{G}$ is discrete if and only if $L^\infty(\mathbb{G})$ contains non-zero compact operators on $L^2(\mathbb{G})$. As a corollary we classify all discrete quantum groups among…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

In this paper we study higher Deligne--Lusztig representations of reductive groups over finite quotients of discrete valuation rings. At even levels, we show that these geometrically constructed representations coincide with certain induced…

Let $G$ be a $p$-adic analytic pro-$p$ group of dimension $d$. We produce an approximate series which descends regularly in strata and whose terms deviate from the lower $p$-series in a uniformly bounded way. This brings to light a new set…

We characterize finite groups G generated by orthogonal transformations in a finite-dimensional Euclidean space V whose fixed point subspace has codimension one or two in terms of the corresponding quotient space V/G with its quotient…

Let $G$ be a semisimple real algebraic Lie group of real rank at least two and $U$ be the unipotent radical of a non-trivial parabolic subgroup. We prove that a discrete Zariski dense subgroup of $G$ that contains an irreducible lattice of…

We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…

We study discrete orderings in the real spectrum of a commutative ring by defining discrete prime cones and give an algebro-geometric meaning to some kind of diophantine problems over discretely ordered rings. Also for a discretely ordered…