Standard Monomial Theory for Bott-Samelson Varieties of GL(n)

We construct an explicit basis for the coordinate ring of the Bott-Samelson variety Z_i associated to G = GL(n) and an arbitrary sequence of simple reflections i. Our basis is parametrized by certain standard tableaux and generalizes the Standard Monomial basis for Schubert varieties. Our standard tableaux have a natural crystal graph structure.Comment: Northeastern University, [email protected] AMSTeX amspp

Wahl's conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians

It is shown that the proof by Mehta and Parameswaran of Wahl's conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians

Standard Monomial Theory for Bott-Samelson Varieties

this paper, we extend the techniques of [19] to give explicit bases for the generalized Demazure modules associated to Bott-Samelson varieties, thus proving a strengthened form of the results announced by the rst and third authors in [12]. (See also [13].) We also obtain more elementary proofs of the cohomology vanishing theorems of Kumar [10] and Mathieu [24]; of the projective normality of Bott-Samelson varieties; and of the Demazure character formula