Osaka Journal of Mathematics

Factorial $P$- and $Q$-Schur functions represent equivariant quantum Schubert classes

Takeshi Ikeda, Leonardo C. Mihalcea, and Hiroshi Naruse

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Abstract

We find presentations by generators and relations for the equivariant quantum cohomology rings of the maximal isotropic Grassmannians of types B, C and D, and we find polynomial representatives for the Schubert classes in these rings. These representatives are given in terms of the same Pfaffian formulas which appear in the theory of factorial $P$- and $Q$-Schur functions. After specializing to equivariant cohomology, we interpret the resulting presentations and Pfaffian formulas in terms of Chern classes of tautological bundles.

Article information

Source
Osaka J. Math., Volume 53, Number 3 (2016), 591-619.

Dates
First available in Project Euclid: 5 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1470413980

Mathematical Reviews number (MathSciNet)
MR3533459

Zentralblatt MATH identifier
1375.14168

Subjects
Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

Citation

Ikeda, Takeshi; Mihalcea, Leonardo C.; Naruse, Hiroshi. Factorial $P$- and $Q$-Schur functions represent equivariant quantum Schubert classes. Osaka J. Math. 53 (2016), no. 3, 591--619. https://projecteuclid.org/euclid.ojm/1470413980


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