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Strong equivariant positivity for homogeneous varieties and back-stable coproduct coefficients

2023/02/24 by Anderson, David
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.12765

Abstract

Using a transversality argument, we demonstrate the positivity of certain coefficients in the equivariant cohomology and K-theory of a generalized flag manifold. This strengthens earlier equivariant positivity theorems (of Graham and Anderson-Griffeth-Miller) by further constraining the roots which can appear in these coefficients. As an application, we deduce that structure constants for comultiplication in the equivariant K-theory of an infinite flag manifold exhibit an unusual positivity property, establishing conjectures of Lam-Lee-Shimozono. Along the way, we present alternative formulas for the back stable Grothendieck polynomials defined by those authors, as well as a new method for computing the coproduct coefficients.

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