On the quantum cohomology of adjoint varieties

By P. Chaput, N. Perrin. 2009

50 citations recorded by the source corpus.

We study the quantum cohomology of adjoint and coadjoint homogeneous spaces. The product of any two Schubert classes does not involve powers of the quantum parameter greater than 2. With the help of the quantum to classical principle, we give presentations of the quantum cohomology algebras. These algebras are semi‐simple for adjoint non‐coadjoint varieties and some properties of the induced strange duality are shown.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/103425f71a746814796a2b4baf29ceaea4364f45

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In Geometry and Topology

1. P. Chaput
2. Leonardo Constantin Mihalcea
3. N. Perrin
4. Anders Skovsted Buch
5. Alexander Yong
6. Hugh Thomas
7. Damir Yeliussizov
8. Matthew J. Samuel

In Statistical and Nonlinear Physics

1. N. Perrin
2. Leonardo Constantin Mihalcea

Citations in the corpus

• A Chevalley formula for the equivariant quantum $K$-theory of cominuscule varieties (2016, background): “ever, it is not in general true that P(V) has isolated T-fixed points. For example, this fails when Xis an adjoint flag variety in the sense that V = Lie(G) is the adjoint representation of G, see e.g. [18]. 5.3. Equivariant quantum K-theory. We finally show that the ring QKT (X) is uniquely determined”
• Finiteness of cominuscule quantum K-theory (2010, background): “The same is true if X is any adjoint variety [8].”