A standard monomial basis for the variety of nilpotent matricesV LakshmibaiNortheastern University
September 25,

ABSTRACT


We construct a "standard monomial basis" for the coordinate ring of the variety of nilpotent matrices in the space M(n) of n by n matrices (over a field of characteristic 0). For this construction, using a result of Lusztig, we identify the variety of nilpotent matrices with a open subset of a Schubert variety in the affine grassmannian \hat{Gr}_n. We then use the Plucker coordinates on the affine grassmannian \hat{Gr}_n, and construct the required basis as certain monomials in the Plucker coordinates (in the same spirit as that of Hodge's work on the classical Grassmannian.). As a consequence, we obtain some interesting connections between our basis and Schur functions & Yamanouchi words. Joint meeting with Lie Theory Seminar 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

