Quantum K-theory Chevalley formula for flag varieties
Quantum K-theory Chevalley formula for flag varieties
Let be a flag variety with Weyl group , let be a simple reflection, and let denote its quantum K-theory ring. For a root , let be the quantum Bruhat operator, and let be a -chain of roots. The notation denotes the corresponding basis element of .
Quantum K-theory Chevalley conjecture. For every ,
where denotes the product in the ring .
This conjecture proposes a Chevalley-type formula for quantum K-theory of the flag variety, extending the corresponding quantum cohomology formula. The supplied source does not state whether it has been proved or disproved.
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Sources & referencesView supporting material
Primary source
Cristian Lenart and Alexander Postnikov, “Affine Weyl groups in K-theory and representation theory”, arXiv:math/0309207 (2005).
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