A Pieri formula and a factorization formula for sums of K-theoretic k-Schur functions

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Abstract

We give a Pieri-type formula for the sum of K-k-Schur functions Pµ6λ gµ(k) over a principal order ideal of the poset of k-bounded partitions under the strong Bruhat order, whose sum we denote by egλ(k). As an application of this, we also give a k-rectangle factorization formula egR(k t)∪λ = egR(k t)egλ(k) where Rt = (tk+1-t), analogous to that of k-Schur functions s(Rkt) ∪λ = s(Rkt) sλ(k)

Original languageEnglish
Pages (from-to)447-480
Number of pages34
JournalAlgebraic Combinatorics
Volume2
Issue number4
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • Affine symmetric groups
  • Coxeter groups
  • K-theoretic k-Schur functions
  • Pieri rule

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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