A standard monomial basis for the variety of nilpotent matrices

V Lakshmibai

Northeastern University

September 25,
refreshments at 3:45pm


We construct a "standard monomial basis" for the co-ordinate 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 co-ordinates on the affine grassmannian \hat{Gr}_n, and construct the required basis as certain monomials in the Plucker co-ordinates (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

Speaker's Contact Info: lakshmibai(at-sign)neu.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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