Puzzles in K-homology of grassmannians

Pavlo Pylyavskyy, Jed Yang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Knutson, Tao, and Woodward (2004) formulated a Littlewood-Richardson rule for the cohomology ring of Grassmannians in terms of puzzles. Vakil (2006) and Wheeler and Zinn-Justin (2017) have found additional triangular puzzle pieces that allow one to express structure constants for K-theory of Grassmannians. Here we introduce two other puzzle pieces of hexagonal shape, each of which gives a Littlewood-Richardson rule for K-homology of Grassmannians. We also explore the corresponding eight versions of Ktheoretic Littlewood-Richardson tableaux.

Original languageEnglish (US)
Pages (from-to)703-727
Number of pages25
JournalPacific Journal of Mathematics
Volume303
Issue number2
DOIs
StatePublished - 2019

Bibliographical note

Funding Information:
We are grateful to Allen Knutson and Joel Lewis for helpful conversations. We thank the anonymous referee for careful reading and useful suggestions. Pylyavskyy is partially supported by NSF grant DMS-1351590 and Sloan Fellowship. Yang is partially supported by NSF RTG grant NSF/DMS-1148634.

Keywords

  • Grassmannian
  • Hexagon
  • K-theory
  • Littlewood-richardson coefficient
  • Puzzles
  • Tiling

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