Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions

Abstract

The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and we prove that this generalization still defines symmetric functions. For this fact, we give two self-contained proofs, one of which constructs a family of involutions on the set of reverse plane partitions generalizing the Bender-Knuth involutions on semistandard tableaux, whereas the other classifies the structure of reverse plane partitions with entries 1 and 2.

29 pages. Ancillary files contain an alternative version with different exposition (including some material on the diamond lemma, which is implicit in the main version of the paper). Comments are welcome!

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