We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space ∆ ⊗⊗ k V . Here ∆ is the fundamental representation of Pin(N) and V is the natural (vector) representation of the orthogonal group O(N). We consider the centralizer algebra CPk = EndPin(N)(∆ ⊗⊗k V ) for Pin(N), the double covering group of O(N) and define...

Olshanski' s centralizer construction provides a realization of the Yangian Y(m) for the Lie algebra gl(m) as a subalgebra in the projective limit algebra A m = lim proj A m (n) as n → ∞, where A m (n) is the centralizer of gl(n − m) in the enveloping algebra U(gl(n)). We give a modified version of this construction based on a quantum analog of Sylvester's theorem. We then use it to get an alge...

a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is ‎cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq‎ ‎z(g)$‎. ‎in this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{cac}$-$p$-groups‎.

In this work we introduce a concept of expansiveness for actions connected Lie groups. We study some its properties and investigate implications expansiveness. the centralizer expansive CW-expansiveness pseudo-group actions. As an application, prove positiveness geometric entropy foliations group

We study cocompleteness, co-wellpoweredness, and generators in the centralizer category of an object or morphism a monoidal category, center weak category. explicitly give some answers for when colimits, these categories can be inherited from their base monidal categories. Most importantly, we investigate cofree objects comonoids

In this paper we construct canonical bases for the Birman-Wenzl algebra BWn, the q-analogue of the Brauer centralizer algebra, and so define left, right and two-sided cells. We describe these objects combinatorially (generalizing the Robinson-Schensted algorithm for the symmetric group) and show that each left cell carries an irreducible representation of BWn. In particular, we obtain canonical...

In a 1989 paper [HW1], Hanlon and Wales showed that the algebra structure of the Brauer Centralizer Algebra A f is completely determined by the ranks of certain combinatorially defined square matrices Z, whose entries are polynomials in the parameter x. We consider a set of matrices M found by Jockusch that have a similar combinatorial description. These new matrices can be obtained from the or...

Every finite non-abelian group of order n has a non-central element whose centralizer exceeding n1/3. The proof does not rely on the classification simple groups, yet it uses Feit-Thompson theorem.