Algebra & Number Theory

A formalism for equivariant Schubert calculus

Dan Laksov

Full-text: Open access

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.

Article information

Source
Algebra Number Theory, Volume 3, Number 6 (2009), 711-727.

Dates
Received: 17 February 2009
Revised: 26 June 2009
Accepted: 6 August 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513797471

Digital Object Identifier
doi:10.2140/ant.2009.3.711

Mathematical Reviews number (MathSciNet)
MR2579392

Zentralblatt MATH identifier
1186.14057

Subjects
Primary: 14N15: Classical problems, Schubert calculus
Secondary: 57R91: Equivariant algebraic topology of manifolds 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

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

Citation

Laksov, Dan. A formalism for equivariant Schubert calculus. Algebra Number Theory 3 (2009), no. 6, 711--727. doi:10.2140/ant.2009.3.711. https://projecteuclid.org/euclid.ant/1513797471


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