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- W3179927852 abstract "Abstract We prove an explicit inverse Chevalley formula in the equivariant K -theory of semi-infinite flag manifolds of simply laced type. By an ‘inverse Chevalley formula’ we mean a formula for the product of an equivariant scalar with a Schubert class, expressed as a $mathbb {Z}left [q^{pm 1}right ]$ -linear combination of Schubert classes twisted by equivariant line bundles. Our formula applies to arbitrary Schubert classes in semi-infinite flag manifolds of simply laced type and equivariant scalars $e^{lambda }$ , where $lambda $ is an arbitrary minuscule weight. By a result of Stembridge, our formula completely determines the inverse Chevalley formula for arbitrary weights in simply laced type except for type $E_8$ . The combinatorics of our formula is governed by the quantum Bruhat graph, and the proof is based on a limit from the double affine Hecke algebra. Thus our formula also provides an explicit determination of all nonsymmetric q -Toda operators for minuscule weights in ADE type." @default.
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- W3179927852 date "2021-01-01" @default.
- W3179927852 modified "2023-09-27" @default.
- W3179927852 title "Inverse<i>K</i>-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type" @default.
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- W3179927852 doi "https://doi.org/10.1017/fms.2021.45" @default.
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