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Schubert Polynomials and Quiver Formulas

Anders Skovsted Buch·Andrew Kresch·Harry Tamvakis·Alexander Yong
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Abstract

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 Schützenberger.

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Anders Skovsted Buch, Andrew Kresch, Harry Tamvakis, Alexander Yong. 2002-11-19. Schubert Polynomials and Quiver Formulas. https://arxiv.org/abs/math/0211300

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