Gröbner geometry of formulae for Schubert polynomials
Ezra Miller
MIT
September 29,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

Schubert polynomials represent cohomology classes of certain subvarieties
of flag manifolds. Results of BilleyJockuschStanley, FominKirillov,
and BergeronBilley show why these polynomials have nonnegative integer
coefficients, by producing combinatorial formulae for them involving
``rcgraphs''. These are subsets of [n]x[n] defined in terms of reduced
expressions for permutations. In this talk, I'll explain how rcgraphs
represent coordinate subspaces in the vector space of n x n matrices, by
showing that the determinants defining Schubert rank conditions are a
Gröbner basis. This gives a new geometric proof of positivity, and
produces as a corollary simple expressions for double Schubert
polynomials. The proof is based on ordinary and equivariant Ktheory of
flag manifolds, via properties of Grothendieck polynomials. This is
joint work with Allen Knutson.

Speaker's Contact Info: ezra(atsign)math.mit.edu
Return to seminar home page
Page loaded on August 31, 2000 at 10:18 PM.

Copyright © 199899, Sara C. Billey.
All rights reserved.

