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Chevalley formulae for
motivic Chern classes of Schubert cells and for stable
envelopes
Leonardo C. Mihalcea, Hiroshi Naruse and Changjian Su |
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Vol. 20 (2026), No. 3, 477–523
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DOI: 10.2140/ant.2026.20.477
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Abstract |
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We prove a Chevalley formula to multiply the motivic Chern classes of Schubert cells in a generalized flag manifold by the class of any line bundle . Our formula is given in terms of the -chains of Lenart and Postnikov. Its proof relies on a change of basis formula in the affine Hecke algebra due to Ram, and on the Hecke algebra action on torus-equivariant K-theory of the complete flag manifold via left Demazure–Lusztig operators. We revisit some wall-crossing formulae for the stable envelopes in . We use our Chevalley formula, and the equivalence between motivic Chern classes of Schubert cells and K-theoretic stable envelopes in , to give formulae for the change of polarization, and for the change of slope for stable envelopes. We prove several additional applications, including Serre, star, and Dynkin, dualities of the Chevalley coefficients, new formulae for the Whittaker functions, and for the Hall–Littlewood polynomials. We also discuss positivity properties of Chevalley coefficients, and properties of the coefficients arising from multiplication by minuscule weights. |
Keywords
motivic Chern classes of Schubert cells, stable envelopes,
$\lambda$-chains, Hecke algebra, Demazure–Lusztig operators
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Mathematical Subject Classification
Primary: 14C17, 14M15
Secondary: 14N15, 17B10, 33D80
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Milestones
Received: 12 February 2024
Revised: 6 March 2024
Accepted: 3 March 2025
Published: 24 March 2026
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Authors |
| Leonardo C. Mihalcea | |
| Department of Mathematics Virginia Tech University Blacksburg, VA United States |
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| Hiroshi Naruse | |
| Graduate School of Education University of Yamanashi Kofu Japan |
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| Changjian Su | |
| Yau Mathematical Sciences
Center Tsinghua University Beijing China |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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