IUMJ

Title: Splitting algebras and Schubert calculus

Authors: Dan Laksov and Anders Thorup

Issue: Volume 61 (2012), Issue 3, 1253-1312

Abstract:

We continue previous work on Schubert calculus of Grassmann schemes via splitting and factorization algebras. The aim of the project is to describe the intersection theory of flag schemes under very general conditions. In this part we extend, generalize, and refine the previous work. Among the main accomplishments of this article is the introduction of Schur determinants generalizing Schur polynomials. For the Schur determinants we obtain determinantal formulas, polarity formulas, and Gysin formulas in great generality. Our main tools are, as in our previous works, splitting and factorization algebras, residues of finite sets of Laurent series, and Gysin maps. The tools provide flexible techniques, useful in many parts of algebra, combinatorics, geometry and representation theory.