Schubert Polynomials and Quiver Formulas

Details Schubert Polynomials and Quiver Formulas Schubert Polynomials and Quiver Formulas

2002-11-19

arxiv.org/abs/math/0211300v1

Duke Math Journal, Volume 122, Issue 1, 125-143 (2004)

Mathematics

Algebraic Geometry

13 pages

Scientific paper

The work of Buch and Fulton established a formula for a general kind of degeneracy locus associated to an oriented quiver of type $A$. The main ingredients in this formula are Schur determinants and certain integers, the quiver coefficients, which generalize the classical Littlewood-Richardson coefficients. Our aim in this paper is to prove a positive combinatorial formula for the quiver coefficients when the rank conditions defining the degeneracy locus are given by a permutation. In particular, this gives new expansions for Fulton's universal Schubert polynomials and the Schubert polynomials of Lascoux and Sch\"utzenberger.

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