Back stable K-theory Schubert calculus

Lam, Thomas; Lee, Seung Jin; Shimozono, Mark

doi:10.48550/arxiv.2108.10202

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Cauchy Identity1

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2021

2022

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Cited by 2 publications

(1 citation statement)

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“…Back-stable Schubert calculus was recently extended to K-theory in [LLS21a]. It would be interesting to see how our approach extends to the K-theory setting.…”

Section: Cauchy Identitymentioning

confidence: 99%

Integrable systems and crystals for edge labeled tableaux

Gunna¹,

Scrimshaw²

2022

Preprint

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We introduce the edge Schur functions E λ that are defined as a generating series over edge labeled tableaux. We formulate E λ as the partition function for a solvable lattice model, which we use to show they are symmetric polynomials and derive a Cauchy-type identity with factorial Schur polynomials. Finally, we give a crystal structure on edge labeled tableau to give a positive Schur polynomial expansion of E λ and show it intertwines with an uncrowding algorithm.

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“…Back-stable Schubert calculus was recently extended to K-theory in [LLS21a]. It would be interesting to see how our approach extends to the K-theory setting.…”

Section: Cauchy Identitymentioning

confidence: 99%

Integrable systems and crystals for edge labeled tableaux

Gunna¹,

Scrimshaw²

2022

Preprint

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Grothendieck to Lascoux expansions

Shimozono¹,

Yu²

2021

Preprint

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We establish the conjecture of Reiner and Yong for an explicit combinatorial formula for the expansion of a Grothendieck polynomial into the basis of Lascoux polynomials. This expansion is a subtle refinement of its symmetric function version due to Buch, Kresch, Shimozono, Tamvakis, and Yong, which gives the expansion of stable Grothendieck polynomials indexed by permutations into Grassmannian stable Grothendieck polynomials. Our expansion is the K-theoretic analogue of that of a Schubert polynomial into Demazure characters, whose symmetric analogue is the expansion of a Stanley symmetric function into Schur functions. Our expansions extend to flagged Grothendieck polynomials.

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Back stable K-theory Schubert calculus

Cited by 2 publications

References 40 publications

Integrable systems and crystals for edge labeled tableaux

Integrable systems and crystals for edge labeled tableaux

Grothendieck to Lascoux expansions

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