Quantum cohomology of orthogonal Grassmannians

By Andrew Kresch, Harry Tamvakis. Compositio Mathematica, 2003

60 citations recorded by the source corpus.

Let V be a vector space with a non-degenerate symmetric form and OG be the orthogonal Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH*(OG) and show that its product structure is determined by the ring of $\widetilde{P}$-polynomials. A ‘quantum Schubert calculus’ is formulated, which includes quantum Pieri and Giambelli formulas, as well as algorithms for computing Gromov--Witten invariants. As an application, we show that the table of three-point, genus zero Gromov–Witten invariants for OG coincides with that for a corresponding Lagrangian Grassmannian LG, up to an involution.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cdb4244cdb7573b06570313fede4b5c41ebe14b4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Gromov-Witten invariants on Grassmannians (2003, methodology): “In the following sections we will mostly adopt the notational conventions of [KT1] and [KT2].”
Quantum Cohomology of Minuscule Homogeneous Spaces (2006, background): “Of course, in degree smaller than 12, this is also the case of the Giambelli type formulas given in the proof of Proposition 3. The coincidence of classical and quantum Giambelli formulas already appeared for minuscule homogeneous varieties of classical type (see [Be], [ KT2 ]).”
Quantum Pieri rules for isotropic Grassmannians (2008, methodology): “The proofs of the quantum Pieri rules in this article use the kernel–span and dimension counting ideas of the first author [Bu] in an essential way; the earlier papers [Be, KT1, KT2 ] used intersection theory on certain Quot scheme compactifications of the moduli space of maps from the projective l”