Puzzles in K-homology of Grassmannians

Pylyavskyy, Pavlo; Yang, Jed

doi:10.2140/pjm.2019.303.703

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…By taking the stable limit of n → ∞, Fomin and Kirillov [7,8] initiated the study of stable Grothendieck functions, where they also replaced the sign corresponding to the degree by a parameter β (which corresponds to taking the connective K-theory [11]). Stable Grothendieck functions have been well-studied using a variety of methods; see for example [1,3,4,5,9,12,13,14,15,19,23,26,27,28,29,30,31,32,33,34,35,41,43] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Crystal structures for canonical Grothendieck functions

Hawkes¹,

Scrimshaw²

2020

Algebraic Combinatorics

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We give a Uq(sln)-crystal structure on multiset-valued tableaux, hook-valued tableaux, and valued-set tableaux, whose generating functions are the weak symmetric, canonical, and dual weak symmetric Grothendieck functions, respectively. We show the result is isomorphic to a (generally infinite) direct sum of highest weight crystals, and for multiset-valued tableaux and valued-set tableaux, we provide an explicit bijection. As a consequence, these generating functions are Schur positive; in particular, the canonical Grothendieck functions, which was not previously known. We also give an extension of Hecke insertion to express a dual stable Grothendieck function as a sum of Schur functions.

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