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Equivariant $K$-theory of Grassmannians II: the Knutson–Vakil conjecture

Part of: Algebraic combinatorics Special varieties

Published online by Cambridge University Press:  09 March 2017

Oliver Pechenik  and
Alexander Yong
Oliver Pechenik
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA email [email protected]
Alexander Yong
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA email [email protected]
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Abstract

In 2005, Knutson–Vakil conjectured a puzzle rule for equivariant $K$-theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors’ recently proved tableau rule for the same Schubert calculus problem.

Keywords

Grassmannianequivariant K-theorypuzzleSchubert calculusLittlewood–Richardson rule

MSC classification

Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds
Secondary: 05E05: Symmetric functions and generalizations 05E15: Combinatorial aspects of groups and algebras
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 4 , April 2017 , pp. 667 - 677
Copyright
© The Authors 2017 

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