Let G be a complex connected reductive group which is defined over R, let G be its Lie algebra, and T the variety of maximal tori of G. For Î¾ âˆˆ G(R), let TÎ¾ be the variety of tori in T whose Lieâ€¦ (More)

Let W be a finite Coxeter group, realized as a group generated by reflections in the /-dimensional Euclidean space V. Let s/ be the hyperplane arrangement in C* = F(g)RC consisting of theâ€¦ (More)

We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomologyâ€¦ (More)

We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points overâ€¦ (More)

We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutativeâ€¦ (More)

This theorem has numerous applications to representation theory and other areas of mathematics (cf. [2, 3, 4, 5, 13]). The proof originally given by Steinberg in [15] involved the algebra ofâ€¦ (More)

Let G be a connected reductive algebraic group over an algebraic closure F of the finite field Fq of q elements; assume G has an Fq-structure with associated Frobenius endomorphism F and let l be aâ€¦ (More)

Let W be a crystallographic Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W , and its weight lattice. The real locusâ€¦ (More)