Let G be a connected linear semisimple Lie group with Lie algebra g and maximal compact subgroup K. Let K C → Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that O is a nilpotent K C -orbit in p C , and O is its Zariski closure in p C . We study the K-type decomposition of the ring of regular functions on O when O is sph...

An MC group is a group in which all chains of centralizers have finite length. In this article, we show that every nilpotent subgroup of an MC group is contained in a definable subgroup which is nilpotent of the same nilpotence class. Definitions are uniform when the lengths of chains are bounded.

We consider a group-theoretic analogue of the classic subset sum problem. It is known that every virtually nilpotent group has polynomial time decidable subset sum problem. In this paper we use subgroup distortion to show that every polycyclic non-virtually-nilpotent group has NP-complete subset sum problem.

We explain a general theory of W-algebras in the context supersymmetric vertex algebras. describe structure associated with odd nilpotent elements Lie superalgebras terms their free generating sets. As an application, we produce explicit generators W-algebra principal element superalgebra $$\mathfrak {gl}(n+1|n)$$ .

Superfield constraints were often used in the past, in particular to describe the AkulovVolkov action of the goldstino by a superfield formulation with L=(ΦΦ)D+[(fΦ)F+h.c.] endowed with the nilpotent constraint Φ = 0 for the goldstino superfield (Φ). Inspired by this, such constraint is often used to define the goldstino superfield even in the presence of additional superfields, for example in ...

We give a new characterization of Lusztig’s canonical quotient, a finite group attached to each special nilpotent orbit of a complex semisimple Lie algebra. This group plays an important role in the classification of unipotent representations of finite groups of Lie type. We also define a duality map. To each pair of a nilpotent orbit and a conjugacy class in its fundamental group, the map assi...

We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The main result says that each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T such that G = U o T , if and only if, for any...

If R is a binomial ring, then a nilpotent R-powered group G is termed power-commutative if for any α ∈ R, [gα, h] = 1 implies [g, h] = 1 whenever gα 6= 1. In this paper, we further contribute to the theory of nilpotent R-powered groups. In particular, we prove that if G is a nilpotent R-powered group of finite type which is not of finite π-type for any prime π ∈ R, then G is PC if and only if i...

It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some F-basis of G and that the group of o-automorphisms of such a group is itself a group of the same kind: Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of o-automorphisms of an ordered, polycyclic group is nilpoten...

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group algebra of a nilpotent group.