Universal Gysin formulas for the universal
                    Hall-Littlewood functions

Nakagawa, Masazumi; Naruse, Hiroshi

doi:10.1090/conm/708/14267

Cited by 13 publications

(5 citation statements)

References 52 publications

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“…For Grassmann bundles this is indeed the case and one can choose between the resolutions constructed through towers of projective bundles or those constructed through towers of Grassmann bundles. The first approach, which results in an ideal sequel of this paper, was developed in [24] by Hudson-Matsumura, while the second was carried out in [45] by Nakagawa-Naruse.…”

Section: Beyond K-theory: Generalized Cohomology Theoriesmentioning

confidence: 99%

Degeneracy loci classes in K-theory — determinantal and Pfaffian formula

Hudson

Ikeda

Matsumura

et al. 2017

Advances in Mathematics

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We prove a determinantal formula and Pfaffian formulas that respectively describe the K-theoretic degeneracy loci classes for Grassmann bundles and for symplectic Grassmann and odd orthogonal bundles. The former generalizes Damon-Kempf-Laksov's determinantal formula and the latter generalize Pragacz-Kazarian's formula for the Chow ring. As an application, we introduce the factorial GΘ/GΘ ′ -functions representing the torus equivariant K-theoretic Schubert classes of the symplectic and the odd orthogonal Grassmannians, which generalize the (double) theta polynomials of Buch-Kresch-Tamvakis and Tamvakis-Wilson.

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Section: Beyond K-theory: Generalized Cohomology Theoriesmentioning

confidence: 99%

Degeneracy loci classes in K-theory — determinantal and Pfaffian formula

Hudson

Ikeda

Matsumura

et al. 2017

Advances in Mathematics

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“…After our work was completed, we were informed by Nakagawa-Naruse that in [17] they achieved, by considering a different resolution, a stable generalisation of the Hall-Littlewood type formulas for Schur polynomials in the context of topological cobordism (cf. [18]).…”

Section: Introductionmentioning

confidence: 99%

Segre classes and Damon–Kempf–Laksov formula in algebraic cobordism

Hudson

Matsumura

2019

Math. Ann.

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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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Universal Gysin formulas for the universal Hall-Littlewood functions

Cited by 13 publications

References 52 publications

Degeneracy loci classes in K-theory — determinantal and Pfaffian formula

Degeneracy loci classes in K-theory — determinantal and Pfaffian formula

Segre classes and Damon–Kempf–Laksov formula in algebraic cobordism

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

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