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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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

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

First available in Project Euclid: 5 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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