Related papers: A construction of pseudo-reductive groups with non…

In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…

Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…

A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…

Based on previous results on the classification of finite-dimensional Nichols algebras over dihedral groups and the characterization of simple modules of Drinfeld doubles, we compute the irreducible characters of the Drinfeld doubles of…

We discuss a certain class of absolutely irreducible group representations that behave nicely under the restriction to normal subgroups and subalgebras. These representations proved to be useful for the construction of abelian varieties…

We study simple non-weight ${\mathfrak{sl}}(2)$-modules which are finitely generated as ${\mathbb C}[z]$-modules. We show that they are described in terms of semilinear endomorphisms and prove that the Smith type induces a stratification on…

A conjecture going back to the eighties claims that there are no non-trivial self-extensions of irreducible modules over symmetric groups if the characteristic of the ground field is not equal to $2$. We obtain some partial positive results…

We give a description of a finite group whose maximal subgroups possess only soluble proper subgroups, which implies the answer to the well-known question on composition factors of finite groups, whose second maximal subgroups are soluble.

Given a semisimple group over a local field of residual characteristic p, its topological group of rational points admits maximal pro-p-subgroups. Quasi-split simply-connected semisimple groups can be described in the combinatorial terms of…

We determine the structure of 2-blocks with minimal nonabelian defect groups, by making use of the classification of finite simple groups.

We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and…

We produce an example of an irreducible discrete subgroup in the product $SL(2,\R)\times SL(2,\R)$ which is not a lattice. This answers a question asked in [15].

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

We construct parametric families of (monic) reducible polynomials having two roots very close to each other.

We study irreducible restrictions from modules over symmetric groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. Such results are known when the…

While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…

In this article we study quotients of deformations of simple singularities, and attempt to characterize them in terms of subsystems of simple root systems. The quotient of a semiuniversal deformation of a simple singularity of inhomogeneous…

Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect…

We study simple and projective modules of a certain class of Ehresmann semigroups, a well-studied generalization of inverse semigroups. Let $S$ be a finite right (left) restriction Ehresmann semigroup whose corresponding Ehresmann category…

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…