Splitting algebras and Schubert calculus

TY - JOUR

T1 - Splitting algebras and Schubert calculus

AU - Thorup, Anders

AU - Laksov, Dan

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Faculty of Science

KW - Mathematics

U2 - 10.1512/iumj.2012.61.4791

DO - 10.1512/iumj.2012.61.4791

M3 - Journal article

SN - 0022-2518

VL - 61

SP - 1253

EP - 1312

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 3

ER -