Vol. 3, No. 6, 2009

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
A formalism for equivariant Schubert calculus

Dan Laksov

Vol. 3 (2009), No. 6, 711–727
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