K. Ding studied a class of Schubert varieties Xλ in type A partial flag manifolds, indexed by integer partitions λ and in bijection with dominant permutations. He observed that the Schubert cell structure of Xλ is indexed by maximal rook placements on the Ferrers board Bλ, and that the integral cohomology groups H∗(Xλ; Z), H ∗(Xμ; Z) are additively isomorphic exactly when the Ferrers boards Bλ,...

Covariant differential complexes on quantum linear groups. Abstract We consider the possible covariant external algebra structures for Cartan's 1-forms (Ω) on GL q (N) and SL q (N). Our starting points are that Ω's realize an adjoint representation of quantum group, and all monomials of Ω's possess the unique ordering. For the obtained external algebras we define the differential mapping d poss...

It would be interesting to extend this result by allowing B to have nilpotence class 2 instead of necessarily being abelian. This cannot be done if p = 2 (Example 4.2), but perhaps it is possible for p odd. (It was done by the author ([Gor, p.274]; [HB, III, p.21]) for the special case in which p is odd and [B,B] ≤ A.) However, there is an application of Thompson’s Replacement Theorem that can ...

We prove that the first complex homology of the Johnson subgroup of the Torelli group Tg is a non-trivial, unipotent Tg-module for all g ≥ 4 and give an explicit presentation of it as a Sym • H1(Tg,C)-module when g ≥ 6. We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that th...