We define the degenerate two boundary affine Hecke-Clifford algebra H d , and show it admits a well-defined q ( n ) -linear action on tensor space M ? N V where is natural module for are arbitrary modules Lie superalgebra of Type Q. When irreducible highest weight parameterized by staircase partition single row, respectively, this factors through quotient . then construct explicit quotient, p u...

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, we establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra HQ(q),r(q) on the rth tensor product of Z2-graded Q-vector space V = V0⊗V1 in detail, and examine its restriction to the qanalogue of the alternating group H1Q(q),r(q). In consequence, we find out that if dimV0 = dimV1, then the ce...

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 ...

In this paper, we define the non-centralizer graph associated to a finite group G, as the graph whose vertices are the elements of G, and whose edges are obtained by joining two distinct vertices if their centralizers are not equal. We denote this graph by ΥG. The non-centralizer graph is used to study the properties of the non-commuting graph of an AC-group. We prove that the non-centralizer g...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 95–112. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introdu...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 65–94. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

Let Φ : M −→ g be a proper moment map associated to an action of a compact connected Lie group, G, on a connected symplectic manifold, (M, ω). A collective function is a pullback via Φ of a smooth function on g∗. In this paper we present four new results about the relationship between the collective functions and the G-invariant functions in the Poisson algebra of smooth functions on M . More s...

To classify the finite dimensional pointed Hopf algebras with Weyl group G of E8, we obtain the representatives of conjugacy classes of G and all character tables of centralizers of these representatives by means of software GAP. In this paper we only list character table 47–64. 2000 Mathematics Subject Classification: 16W30, 68M07 keywords: GAP, Hopf algebra, Weyl group, character. 0. Introduc...

where the LGLn(λ) are irreducible GLn(C)-modules and the S λ k are irreducible Sk-modules. The decomposition in (0.1) essentially makes the study of the representations of GLn(C) and the study of representations of the symmetric group Sk two sides of the same coin. The group GLn(C) has interesting subgroups, GLn(C) ⊇ On(C) ⊇ Sn ⊇ Sn−1, and corresponding centralizer algebras, CSk ⊆ CBk(n) ⊆ CAk(...