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arXiv · 1607.03524

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

Seth Baldwin·Shrawan Kumar
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Abstract

We prove sign-alternation of the structure constants in the basis of 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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Seth Baldwin, Shrawan Kumar. 2016-07-12. Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II. https://arxiv.org/abs/1607.03524

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