Assume Mn is the n-dimensional permutation module for the symmetric group Sn, and let M n be its k-fold tensor power. The partition algebra Pk(n) maps surjectively onto the centralizer algebra EndSn(M ⊗k n ) for all k, n ∈ Z≥1 and isomorphically when n ≥ 2k. We describe the image of the surjection Φk,n : Pk(n) → EndSn(M ⊗k n ) explicitly in terms of the orbit basis of Pk(n) and show that when 2...

Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbers. The same holds for a Sylow 2-subgroup of C.

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent...

This paper studies a q-deformation, Br,s(q), of the walled Brauer algebra (a certain subalgebra of the Brauer algebra) and shows that the centralizer algebra for the action of the quantum group UR(gln) on mixed tensor space (R) ⊗ (Rn)∗ is generated by the action of Br,s(q) for any commutative ring R with one and an invertible element q.

Let G be a compact connected Lie group and H, the centralizer of a one-parameter subgroup in G. Combining the ideas of Bott-Samelson resolutions of Schubert varieties and the enumerative formula on a twisted product of 2 spheres obtained in [Du2], we obtain a closed formula for multiplying Schubert classes in the flag manifold G/H. 2000 Mathematical Subject Classification: 14N15 (14M10).

The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

In [I] we introduced the notion of transfer from a group over a local field to an associated endoscopic group, but did not prove its existence, nor do we do so in the present paper. Nonetheless we carry out what is probably an unavoidable step in any proof of existence: reduction to a local statement at the identity in the centralizer of a semisimple element, a favorite procedure of Harish Chan...