Quantum Cohomology of Minuscule Homogeneous Spaces

By P. Chaput, Laurent Manivel, N. Perrin. 2006

69 citations recorded by the source corpus.

We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov–Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincaré duality. In particular, we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/40588d44832cc48322268adfc80662441990d321

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

A Chevalley formula for the equivariant quantum $K$-theory of cominuscule varieties (2016, methodology): “The Gromov-Witten invariants of any cominuscule variety X can be computed using the ‘quantum equals classical ’ theorem [12, 17, 13, 19], which states that any (3 point, genus zero) Gromov-Witten invariant of X is equal to a K-theoretic triple intersection on a related space.”
Quantum Cohomology of Minuscule Homogeneous Spaces III Semi-Simplicity and Consequences (2007, background): “Chow ring). See [ CMP1 ], section 4.1, for more details.”
QUANTUM K-THEORY OF GRASSMANNIANS (2008, background): “Part (a) of this lemma is known from [5, Thm.3.3.4(a)], and part (b) is true because f is a flat morphism.”
K-theory of minuscule varieties (2013, unknown): “A G ] 2 3 Ju n 20 13”
Finiteness of cominuscule quantum K-theory (2010, unknown): “A G ] 1 5 Ju n 20 12”
On the quantum cohomology of adjoint varieties (2009, methodology): “For minuscule and cominuscule homogeneous spaces, the quantum cohomology was described in [5] for classical groups and in [9] in general.”
Curve neighborhoods of Schubert varieties (2013, unknown): “The study of this integer was suggested by Zak [27] and plays a fundamental role in Chaput, Manivel, and Perrin’s generalization [9] of the ‘quantum equals classical’ principle from [6].”