On the quantum cohomology of adjoint varieties

Nicolas Perrin; Pierre-Emmanuel Chaput

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On the quantum cohomology of adjoint varieties

Algebraic Geometry · Submitted 30 Apr 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These algebras are semi-simple for adjoint non coadjoint varieties and some properties of the induced strange duality are shown.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.90 · compares with prior results 0.07 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher 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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces.	contribution 0.95	0.89	0.07	asserted 0.85
s1	The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2.	result 1.00	0.74	0.26	asserted 1.00
s2	With the help of the quantum to classical principle we give presentations of the quantum cohomology algebras.	method 0.58	0.94	0.16	asserted 1.00
s3	These algebras are semi-simple for adjoint non coadjoint varieties and some properties of the induced strange duality are shown.	result 0.98	0.88	0.31	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher 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.

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3 arXiv papers cite this in 8 sentences

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Moreover, contrary to what we prove here, the small quantum cohomology ring of the symplectic Grassmannian of lines is not semisimple (see [ref] ), and it is not known whether the Dubrovin conjecture holds in this case.

Quantum cohomology of the odd symplectic Grassmannian of lines · Introduction · 0.97

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