A Pieri formula and a factorization formula for sums of K-theoretic k-Schur functions
Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 447-480.

We give a Pieri-type formula for the sum of K-k-Schur functions μλ g μ (k) over a principal order ideal of the poset of k-bounded partitions under the strong Bruhat order, whose sum we denote by g ˜ λ (k) . As an application of this, we also give a k-rectangle factorization formula g ˜ R t λ (k) =g ˜ R t (k) g ˜ λ (k) where R t =(t k+1-t ), analogous to that of k-Schur functions s R t λ (k) =s R t (k) s λ (k) .

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DOI: 10.5802/alco.45
Classification: 05E05, 20F55
Keywords: $K$-theoretic $k$-Schur functions, Pieri rule, Coxeter groups, affine symmetric groups

Takigiku, Motoki 1

1 Graduate School of Mathematical Sciences the University of Tokyo Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Takigiku, Motoki. A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 447-480. doi : 10.5802/alco.45. https://alco.centre-mersenne.org/articles/10.5802/alco.45/

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