Motivic characteristic classes in cohomological Hall algebras

摘要: The equivariant Chern-Schwartz-MacPherson (CSM) class and the Motivic Chern (MC) are important characteristic classes of singular varieties in cohomology K theory---and their theory overlaps with Okounkov's stable envelopes. We study CSM MC for orbits Dynkin quiver representations. show that problem computing all these can be reduced to some basic $c^o_\beta$, $C^o_\beta$ parameterized by positive roots $\beta$. prove an identity a deformed version Kontsevich-Soibelman's Cohomological (and K-theoretic) Hall Algebra (CoHA, KHA), namely, product exponentials $c^o_\beta$ (or $C^o_\beta$) formally depending on stability function Z, does not depend Z. This identity---which encodes infinitely many identities among rational functions growing number variables---has structure Donaldson-Thomas type quantum dilogarithm identities. Using wall-crossing argument we present as certain commutators CoHA, KHA.