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Mathematics > Algebraic Geometry
Title: Strong equivariant positivity for homogeneous varieties and back-stable coproduct coefficients
(Submitted on 24 Feb 2023)
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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