Vol. 3, No. 6, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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