Discrete Mathematics & Theoretical Computer Science |

- 1 Department of Mathematics and Statistics [Albany-USA]
- 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 Graham-Willems 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 Graham-Willems, 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 Kazhdan-Lusztig basis of the corresponding Hecke algebra.

Source: HAL:hal-01337776v1

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)

Section: Proceedings

Published on: January 1, 2015

Imported on: November 21, 2016

Keywords: Schubert classes,Bott-Samelson classes,elliptic cohomology,root polynomial,Kazhdan-Lusztig basis,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Funding:

- Source : OpenAIRE Graph
*Combinatorics of Crystals, Macdonald Polynomials, and Schubert Calculus*; Funder: National Science Foundation; Code: 1101264- Funder: Natural Sciences and Engineering Research Council of Canada
*Representation Theory and Schubert Calculus: Combinatorics and Interactions*; Funder: National Science Foundation; Code: 1362627

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