Cristian Lenart ; Kirill Zainoulline

On Schubert calculus in elliptic cohomology
dmtcs:2502 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2015,
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)

https://doi.org/10.46298/dmtcs.2502
1 Department of Mathematics and Statistics [AlbanyUSA]
2 Department of Mathematics and Statistics [Ottawa]
An important combinatorial result in equivariant cohomology and $K$theory Schubert calculus is represented by the formulas of Billey and GrahamWillems for the localization of Schubert classes at torus fixed points. These formulas work uniformly in all Lie types, and are based on the concept of a root polynomial. We define formal root polynomials associated with an arbitrary formal group law (and thus a generalized cohomology theory). We usethese polynomials to simplify the approach of Billey and GrahamWillems, as well as to generalize it to connective $K$theory and elliptic cohomology. Another result is concerned with defining a Schubert basis in elliptic cohomology (i.e., classes independent of a reduced word), using the KazhdanLusztig basis of the corresponding Hecke algebra.