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Motivic Chern classes and K-theoretic stable envelopes
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We study a K-theoretic characteristic class of singular varieties, namely the equivariant motivic Chern class. We prove that the motivic Chern class is characterized by an 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. Lastly, we calculate the equivariant motivic Chern class of the orbits of the A2 quiver representation, which yields formulas for the motivic Chern classes of determinantal varieties and more general degeneracy loci.
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Characteristic classes of symmetric and skew-symmetric degeneracy loci
Explicit formulas for Chern-Schwartz-MacPherson classes of all GL_n(C)-orbits in symmetric and skew-symmetric matrices, via a sieve method and an interpolation method.
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