Motivic Chern classes and K-theoretic stable envelopes

Abstract

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.

References in corpus (18)

• Quantum Groups and Quantum Cohomology
• Equivariant Chern classes of singular algebraic varieties with group actions
• Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety
• Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
• Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells
• A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes
• Chern-Schwartz-MacPherson classes for Schubert cells in flag manifolds
• Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology
• Chern classes of Schubert cells and varieties
• Chern-Schwartz-MacPherson classes of degeneracy loci
• Motivic Chern classes of Schubert cells, Hecke algebras, and applications to Casselman's problem
• Equivariant characteristic classes of singular complex algebraic varieties
• Riemann-Roch for Deligne-Mumford stacks
• Chern classes of birational varieties
• On the K-theory stable bases of the Springer resolution
• The incidence class and the hierarchy of orbits
• Quantum difference equation for Nakajima varieties
• Residues, Grothendieck polynomials and K-theoretic Thom polynomials

Cited by in corpus (10)

• Elliptic classes of Schubert varieties via Bott-Samelson resolution
• Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory
• Positivity of Segre-MacPherson classes
• Bow varieties---geometry, combinatorics, characteristic classes
• From motivic Chern classes of Schubert cells to their Hirzebruch and CSM classes
• Structure constants for Chern classes of Schubert cells
• The positivity of local equivariant Hirzebruch class for toric varieties
• Local Euler Obstructions of Reflective Projective Varieties
• Chevalley formulae for the motivic Chern classes of Schubert cells and for the stable envelopes
• Geometric properties of the Kazhdan-Lusztig Schubert basis