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On Schubert calculus in elliptic cohomology

Abstract : 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 use these 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.
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https://hal.archives-ouvertes.fr/hal-01337776
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Submitted on : Monday, June 27, 2016 - 3:21:08 PM
Last modification on : Monday, October 5, 2020 - 1:14:01 PM

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  • HAL Id : hal-01337776, version 1

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Cristian Lenart, Kirill Zainoulline. On Schubert calculus in elliptic cohomology. 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015), Jul 2015, Daejeon, South Korea. pp.757-768. ⟨hal-01337776⟩

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