A formalism for equivariant Schubert calculus

Laksov, Dan

doi:10.2140/ant.2009.3.711

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A formalism for equivariant Schubert calculus

Dan Laksov

Vol. 3 (2009), No. 6, 711–727

DOI: 10.2140/ant.2009.3.711

Abstract

In previous work we have developed a general formalism for Schubert calculus. Here we show how this theory can be adapted to give a formalism for equivariant Schubert calculus consisting of a basis theorem, a Pieri formula and a Giambelli formula. Our theory specializes to a formalism for equivariant cohomology of grassmannians. We interpret the results in a ring that can be considered as the formal generalized analog of localized equivariant cohomology of infinite grassmannians.

Keywords

equivariqant cohomology, Schubert calculus, quantum cohomology, symmetric polynomials, exterior products, Pieri's formula, Giambelli's formula, GKM condition, factorial Schur functions, grassmannians

Mathematical Subject Classification 2000

Primary: 14N15

Secondary: 57R91, 14M15

Milestones

Received: 17 February 2009

Revised: 26 June 2009

Accepted: 6 August 2009

Published: 20 November 2009

Authors

Dan Laksov
KTH Department of Mathematics 10044 Stockholm Sweden

Vol. 3, No. 6, 2009