Related papers: Compatible intertwiners for representations of fin…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of ${\rm GL}_n(\mathbf{C})$ on the variety of $x$-nilpotent complex matrices and translate it to a representation-theoretic context. We obtain a criterion as…

We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…

Let G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classified. We describe a simple algorithm for finding a…

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal context, like for finite groups, nilpotency is equivalent to…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a…

We treat the topic of the closures of the nilpotent orbits of the Lie algebras of Exceptional groups through their descriptions as moduli spaces, in terms of Hilbert series and the highest weight generating functions for their…

We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also…

In analogy with the Barbasch-Vogan duality for real reductive linear groups, we introduce a duality notion useful for the representation theory of the real metaplectic groups. This is a map on the set of nilpotent orbits in a complex…

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LieNQ) is described. The paper studies graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented,…

We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…

In this paper, we construct and classify the special unipotent representations of a real reductive group attached to the principal nilpotent orbit. We give formulas for the $\mathbf{K}$-types, associated varieties, and Langlands parameters…

We explore finitely generated groups by studying the nilpotent towers and the various Lie algebras attached to such groups. Our main goal is to relate an isomorphism extension problem in the Postnikov tower to the existence of certain…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…

The goal of this diploma thesis is to give a detailed description of Kirillov's Orbit Method for the case of compact connected Lie groups. The theory of Kirillov aims at finding all irreducible unitary representations of a given Lie group…

A linear \'etale representation of a complex algebraic group $G$ is given by a complex algebraic $G$-module $V$ such that $G$ has a Zariski-open orbit on $V$ and $\dim G=\dim V$. A current line of research investigates which \'etale…

A uniform parametrization for the irreducible spin representations of Weyl groups in terms of nilpotent orbits is recently achieved by Ciubotaru (2011). This paper is a generalization of this result to other real reflection groups. Let…