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
On Schubert calculus in elliptic cohomologyArticle

Authors: Cristian Lenart 1; Kirill Zainoulline 2

  • 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.


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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