Positivity in 𝑇-equivariant 𝐾-theory of flag varieties associated to Kac-Moody groups II

Baldwin, Seth; Kumar, Shrawan

doi:10.1090/ert/494

Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II
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by Seth Baldwin and Shrawan Kumar

Represent. Theory 21 (2017), 35-60

DOI: https://doi.org/10.1090/ert/494

Published electronically: March 24, 2017

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Abstract:

We prove sign-alternation of the structure constants in the basis of the structure sheaves of opposite Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the flag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic subgroup. This generalizes the work of Anderson-Griffeth-Miller from the finite case to the general Kac-Moody case, and affirmatively answers a conjecture of Lam-Schilling-Shimozono regarding the signs of the structure constants in the case of the affine Grassmannian.

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