Gysin maps, duality, and Schubert classes

Darondeau, Lionel; Pragacz, Piotr

doi:10.4064/fm588-6-2018

Cited by 4 publications

(1 citation statement)

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“…The explicit computations of the pushforward have been explored through various ways. One of the approaches which have been studied extensively in recent years is to reexpress the right hand side of (1.1) as iterated residues and find various pushforward formulas for polynomials which can be viewed as generalized cohomology classes [47,48,57,58,59,60,61,62,63,64,65,66,67,68,69].…”

Section: Introductionmentioning

confidence: 99%

Integrable models and $K$-theoretic pushforward of Grothendieck classes

Motegi

2020

Preprint

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We show that a multiple commutation relation of the Yang-Baxter algebra of integrable lattice models derived by Shigechi and Uchiyama can be used to connect two types of Grothendieck classes by the K-theoretic pushforward from the Grothendieck group of Grassmann bundles to the Grothendieck group of a nonsingular variety. Using the commutation relation, we show that two types of partition functions of an integrable five-vertex model, which can be explicitly described using skew Grothendieck polynomials, and can be viewed as Grothendieck classes, are directly connected by the K-theoretic pushforward. We show that special cases of the pushforward formula which correspond to the nonskew version are also special cases of the formulas derived by Buch.

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