SCHUBERT PUZZLES AND INTEGRABILITY II: MULTIPLYING MOTIVIC SEGRE CLASSES

Abstract

In Schubert Puzzles and Integrability I we proved several “puzzle rules” for computing products of Schubert classes in K-theory (and sometimes equivariant K-theory) of d-step flag varieties. The principal tool was “quantum integrability”, in several variants of the Yang–Baxter equation; this let us recognize the Schubert structure constants as q → 0 limits of certain matrix entries in products of R (and other) matrices of Qq(g[z±])-representations. In the present work we give direct cohomological interpretations of those same matrix entries but at finite q: they compute products of “motivic Segre classes”, closely related to K-theoretic Maulik–Okounkov stable classes living on the cotangent ..