Séminaire Lotharingien de Combinatoire, 82B.90 (2019), 12 pp.

Rebecca Goldin and Allen Knutson

Schubert structure operators

Abstract. We use operators to reformulate the Andersen-Jantzen-Soergel/Billey formula for the point restrictions of equivariant Schubert classes of the cohomology of G/B. We introduce new operators whose coefficients compute Schubert structure constants (in a manifestly polynomial, but not positive, way), resulting in a formula much like and generalizing the positive AJS/Billey formula. Our proof involves Bott-Samelson manifolds, and in particular, the cohomology basis dual to the homology basis of classes of sub-Bott-Samelson manifolds.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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