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


Authors: Seth Baldwin and Shrawan Kumar
Journal: Represent. Theory 21 (2017), 35-60
MSC (2010): Primary 19L47; Secondary 14M15
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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Additional Information

Seth Baldwin
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
Email: seth.baldwin@unc.edu

Shrawan Kumar
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
Email: shrawan@email.unc.edu

DOI: https://doi.org/10.1090/ert/494
Received by editor(s): December 4, 2016
Published electronically: March 24, 2017
Article copyright: © Copyright 2017 American Mathematical Society