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arXiv · 1909.05283

Schubert structure operators and K_T(G/B)

Rebecca Goldin·Allen Knutson
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Abstract

We prove a formula for the structure constants of multiplication of equivariant Schubert classes in both equivariant cohomology and equivariant K-theory of Kac-Moody flag manifolds G/B. We introduce new operators whose coefficients compute these (in a manifestly polynomial, but not positive, way), resulting in a formula much like and generalizing the positive Andersen-Jantzen-Soergel/Billey and Graham/Willems formulae for the restriction of classes to fixed points. Our proof involves Bott-Samelson manifolds, and in particular, the (K-)cohomology basis dual to the (K-)homology basis consisting of classes of sub-Bott-Samelson manifolds.

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Rebecca Goldin, Allen Knutson. 2019-09-11. Schubert structure operators and K_T(G/B). https://arxiv.org/abs/1909.05283

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