Let g=g0¯⊕g1¯ be a basic classical Lie superalgebra over C, e∈g0¯ nilpotent element and ge the centralizer of e in g. We study various properties elements g, which have previously only been considered case algebras. In particular, we prove that is reachable if satisfies Panyushev property for g=sl(m|n), m≠n or psl(n|n) osp(m|2n). For exceptional superalgebras g=D(2,1;α), G(3), F(4), give classi...

Abstract As a continuation of [9], this paper studies scattered representations $SO(2n+1, {{\mathbb{C}}})$, $Sp(2n, and $SO(2n, {{\mathbb{C}}})$. We describe the Zhelobenko parameters these representations, count their cardinality, determine spin-lowest $K$-types. also disprove conjecture raised in 2015 asserting that unitary dual can be obtained via parabolic induction from irreducible with no...

In this paper, we consider the Rumin complex on homogenenous nilpotent Lie groups. We present an alternative construction to classical one Carnot groups using ideas from parabolic geometry. also give explicit computations for Engel group with approach.

Given any simple Lie superalgebra g, we investigate the structure of an arbitrary simple weight g-module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuper-algebra. Then we classify the cuspidal Levi sub...