Explicit Standard Monomial Basis For Coordinatization Of Schubert Varieties printable pdf download

Explicit Standard Monomial Basis For Coordinatization Of Schubert Varieties

1115-14-298

David C Lax* (dclax@live.unc.edu), Phillips Hall CB#3250, Chapel Hill, NC 27599. Explicit

Standard Monomial Basis for Coordinatization of Schubert Varieties.

The Plucker embedding of the ﬂag manifold is a concrete projective coordinatization using products of minors of a matrix

as coordinates. These products are nicely indexed by tableaux on a Young diagram. Lakshmibai, Musili, and Seshadri

gave a standard monomial basis for the projective coordinates when restricted to a Schubert subvariety. Reiner and

Shimozono made this theory more explicit by giving a straightening algorithm for the products of the minors in terms of

the right key of a semistandard Young tableau. Since then, Willis introduced scanning tableaux as a more direct way to

obtain right keys. We use scanning tableaux to give more-direct proofs of the spanning and the linear independence of

the standard monomials. This basis is a weight basis for the dual of a Demazure module for a Borel subgroup of GL(n).

As a result, we independently obtain an expression for these Demazure characters as sums of weights over the tableaux

used to index the standard monomial basis. (Received September 21, 2015)

Explicit Standard Monomial Basis For Coordinatization Of Schubert Varieties