相关论文: Modular irreducibility of cuspidal unipotent chara…

If chi is an irreducible character of a finite group G then the support of chi is the subset of G on which chi does not vanish. In this note, we study the supports of characters of certain classes of p-groups (a p-group is a finite group of…

We study the representations of the W-algebra W(g) associated to an arbitrary finite-dimensional simple Lie algebra g via the quantized Drinfeld-Sokolov reductions. The characters of irreducible representations with non-degenerate highest…

In this paper, we compute the multiplicities of tensor products of almost unipotent characters and Deligne Lusztig characters of a finite reductive group $G^F$, and these multiplicities are related to the ring structure of the complex…

Let Rep(F;K) denote the category of functors from finite dimensional F-vector spaces to K-modules, where F is a field and K is a commutative ring. We prove that, if F is a finite field, and Char F is invertible in K, then the K-linear…

Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…

We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…

For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our…

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of geometric unipotent radicals of standard pseudo-reductive…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

Let F be a non-archimedean local field of odd residual characteristic p. Let G be a (connected) reductive group that splits over a tamely ramified field extension of F. We show that a construction analogous to Yu's construction of complex…

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent representations of unitary groups over finite fields. We give the first descents of unipotent…

We determine precisely the number of irreducible summands of an irreducible cross characteristic representation of $GL_{n}(q)$ on restriction to $SL_{n}(q)$. Combined with a recent result of C. Bonnafe, this yields a canonical labeling for…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

Let $W$ be a finite Weyl group and $\sg$ be a non-trivial graph automorphism of $W$. We show a remarkable relation between the $\sg$-twisted involution module for $W$ and the Frobenius--Schur indicators of the unipotent characters of a…

We know from Letellier that if for some triple of partitions the corresponding Kronecker coefficient is non-zero then the corresponding multiplicities for unipotent characters of GL(n,q) is also non-zero. A conjecture of Saxl says that the…

To each irreducible infinite dimensional representation $(\pi,\cH)$ of a $C^*$-algebra $\cA$, we associate a collection of irreducible norm-continuous unitary representations $\pi_{\lambda}^\cA$ of its unitary group $\U(\cA)$, whose…

Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called accessibility - is the starting point of…

In the paper we study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group $G$ of nilpotency class 2 admits a faithful irreducible…

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p > 0$. We consider connected reductive subgroups $X$ of $G$ that contain a given distinguished unipotent element $u$ of $G$. A result of…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…