Related papers: The classification of thick representations of sim…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We show that finite quasisimple groups of Lie type in characteristic $p$ with an irreducible representation of prime degree $r$ over a finite field of characteristic $p$ have orders bounded above by a function of $r$, independent of $p$. We…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

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…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…

We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irreducible representations of dimension at most n for a simple…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

The Lie algbera of a compact semisimple Lie group G is determined by the degrees of the irreducible representations of G. However, two different groups can have the same representation degrees.

We determine the finite groups whose real irreducible representations have different degrees.

We initiate a systematic study of the perfection of affine group schemes of finite type over fields of positive characteristic. The main result intrinsically characterises and classifies the perfections of reductive groups, and obtains a…

For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…

Answering a question of I. M. Isaacs, we show that the largest degree of irreducible complex representations of any finite non-abelian simple group can be bounded in terms of the smaller degrees. We also study the asymptotic behavior of…