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A Thom-Porteous formula for connective K-theory using algebraic cobordism

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arxiv 1310.0895 v1 pith:XE2OPSXL submitted 2013-10-03 math.AG

classification math.AG
keywords formularingalgebraiccobordismconnectivek-theorythom-porteousbeta-polynomials
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We prove a formula for the push-forward class of Bott-Samelson resolutions in the algebraic cobordism ring of the flag bundle. We specialise our formula to connective K-theory providing a geometric interpretation to the double beta-polynomials of Fomin and Kirillov by computing the fundamental classes of Schubert varieties. As a corollary we obtain a Thom-Porteous formula generalising those of the Chow ring and of the Grothendieck ring of vector bundles.

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  1. Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\beta$-Grothendieck polynomials

    math-ph 2025-02 conditional novelty 6.0 of 10

    Bethe ansatz states of a new GL(n) five vertex model expand into double β-Grothendieck polynomials, and the model's Bethe equations reproduce the quantum Whitney relations of flag varieties.

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