Related papers: Lifting representations of finite reductive groups…

Let $G \subseteq \tilde{G}$ be two quasisplit connected reductive groups over a local field of characteristic zero and $G_{der} = \tilde{G}_{der}$. Although the existence of L-packets is still conjectural in general, it is believed that the…

Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain…

Let $G$ and $\tilde G$ be reductive groups over a local field $F$. Let $\eta : \tilde G \to G$ be a $F$-homomorphism with commutative kernel and commutative cokernel. We investigate the pullbacks of irreducible admissible…

In 1997, Deligne showed that the reduced lift presentation of a finite type generalized braid group remains correct if it is (suitably) interpreted as a presentation of a topological monoid. In this expository paper, we point out that…

We consider the proportion of zero entries in the character table of a sequence of reductive groups over a finite field. We prove an asymptotic lower bound when the reductive group is fixed and the size of the finite field increases.…

For a representation of a finite group $G$ on a complex vector space $V$ we determine when a holomorphic $\binom{p}{q}$-tensor field on the principle stratum of the orbit space $V/G$ can be lifted to a holomorphic $G$-invariant tensor field…

In this paper we study the universal lifting spaces of local Galois representations valued in arbitrary reductive group schemes when $\ell \neq p$. In particular, under certain technical conditions applicable to any root datum we construct…

Let K be a non-archimedean local field and let G be a connected reductive K-group which splits over an unramified extension of K. We investigate supercuspidal unipotent representations of the group G(K). We establish a bijection between the…

Given a central isogeny $\pi\colon G\to H$ of connected reductive $\overline{\mathbb Q}_p$-groups, and a local Galois representation $\rho$ valued in $H(\overline{\mathbb Q}_p)$ that is trianguline in the sense of Daruvar, we study whether…

Let k be an algebraically closed field of characteristic zero, F its algebraically closed extension, and G be the group of k-automorphisms of F endowed with a natural topology. One of the purposes of this paper is to show that any…

Consider a strictly positively graded finitely generated infinite-dimensional real Lie algebra $\mathfrak{g}$. It has a well-defined Lie group $\overline{\mathbf{G}}$, which is an inverse limit of finite-dimensional nilpotent Lie groups (a…

Given a $p$-adic group $G=\mathbf{G}(F)$ and a finite group $\Gamma\subset\mathrm{Aut}_F(\mathbf{G})$ such that the fixed-point subgroup $\mathbf{G}^\Gamma$ is reductive, we show that every semisimple character (in the sense of Bushnell and…

Let $G_\cpl$ be a connected complex reductive Lie group, and $G$ be a real form. Let $(\pi,V)$ be a finite-dimensional irreducible representation of $G$. Assume $(\pi,V)$ admits a $G$ invariant hermitian form. {In…

In this paper, we interpret the theta rank of an irreducible character of a finite classical group in terms of the data from the Lusztig classification. Then we prove the following two results: (1) the agreement of the $U$-rank and the…

Let \hat G be the semidirect product of a connected reductive group G over F_q with a finite cyclic group generated by a quasisemisimple automorphism of G defined over F_q. In this paper we prove a conjecture of G. Malle concerning the…

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it…

In this series of papers, we investigate properties of a finite group which are determined by its low degree irreducible representations over a number field $F$, i.e. its representations on matrix rings $\operatorname{M}_n(D)$ with $n \leq…

Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.

Lusztig conjectured that the almost characters of a finite reductive group are up to a scalar the same as the characteristic functions of the rational character sheaves defined on the corresponding algebraic group. We propose in this paper…

We define tensor categories ${\sf Ver}_{p^n}(G)$ in characteristic $p$ for connected reductive groups $G$ and positive integers $n$, generalising the semisimple Verlinde categories ${\sf Ver}_p(G)$ originating from Gelfand-Kazhdan and the…