Motivic Chern classes and K-theoretic stable envelopes

Fehér, László and Rimanyi, Richard and Weber, Andrzej (2020) Motivic Chern classes and K-theoretic stable envelopes. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 122 (1). pp. 153-189. ISSN 0024-6115

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Abstract

We consider a smooth algebraic variety with an action of a linear algebraic group acting with finitely many orbits. We study equivariant characteristic classes of the orbits, namely the equivariantmotivic Chern classes, in the K-theory of the ambient space. We prove that the motivic Chern class satisfies the axiom system inspired by that of 'K-theoretic stable envelopes', recently defined by Okounkov and studied in relation with quantum group actions on the K-theory algebra of moduli spaces. We also give explicit formulas for the equivariant motivic Chern classes of Schubert cells and matrix Schubert cells. Finally, we calculate the equivariant motivic Chern class of the orbits of theA2quiver representation, which yields formulas for the motivic Chern classes of determinantal varieties and more general degeneracy loci.

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