We define a class of transversal slices in spaces which are quasi-Poisson for the action complex semisimple group G. This is multiplicative analogue Whittaker reduction. One example universal centralizer Z G, equipped with usual symplectic structure this way. construct smooth relative compactification Z‾ by taking closure each fiber wonderful By realizing as larger variety, we show that it and ...

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of t-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics. 2000 Mat...

A group G is called power commutative, or a PC-group, if [xm, yn] = 1 implies [x, y] = 1 for all x, y ∈G such that xm = 1, yn = 1. So power-commutative groups are those groups in which commutativity of nontrivial powers of two elements implies commutativity of the two elements. Clearly, G is a PC-group if and only if CG(x) = CG(x) for all x ∈ G and all integers n such that xn = 1. Obvious examp...

An Engel sink of an element g a group G is set $${\cal E}(g)$$ such that for every x ∈ all sufficiently long commutators [⋯[[x, g], g],…, g] belong to . (Thus, precisely when we can choose E}(g) = \{ 1\} $$ .) It proved if profinite admits elementary abelian automorphisms A coprime order q2 prime q each {1} the centralizer CG(a) has countable (or finite) sink, then finite normal subgroup N G/N ...

The enveloping algebra U(g) of the Lie superalgebra g has a deformation, called the Yangian of qN . For each M = 1 ,2 , . . . denote by A M N the centralizer of qM ⊂ qN+M in the associative superalgebra U(qN+M ) . We construct a sequence of surjective homomorphisms U(qN ) ← A 1 N ← A 2 N ← . . . . We describe the inverse limit of the sequence of centralizer algebras A1N ,A 2 N , . . . in terms ...

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such as the isomorphism problem of general Coxeter groups. In the argument, some properties of certain special elements and of the fixed-point subgroups by graph...

We compute matrix units for Brauer’s centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except S0(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young’...