Motivic Segre classes of Schubert cells and the connective formal group law

Raj Gandhi

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arXiv · 2605.26556

Motivic Segre classes of Schubert cells and the connective formal group law

Raj Gandhi

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Abstract

We use the connective formal group law to define a one-parameter ($\beta$-)deformation of the motivic Segre classes of Schubert cells in the $d$-step flag variety. This $\beta$-deformation specializes to the motivic Segre classes of Schubert cells when $\beta=1$ and to the Segre-Schwartz-MacPherson classes of Schubert cells when $\beta=0$. We define rational function representatives for the $\beta$-deformed classes in the $d=1$ case in terms of a solvable lattice model, and we prove a combinatorial formula for the structure constants in the $\beta$-deformed basis in the $d=1$ case using Knutson-Tao puzzles. The proof of the puzzle formula involves intertwiners for representations of the multi-parameter quantum group of type $\widehat{a}_2$. We show that our $\beta$-deformations can be viewed as quotients of canonical elements in a quotient of the equivariant algebraic cobordism ring of the cotangent bundle of the flag variety by proving that the canonical elements satisfy a GKM type condition.

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Raj Gandhi. 2026-05-26. Motivic Segre classes of Schubert cells and the connective formal group law. https://arxiv.org/abs/2605.26556

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