ALGEBRAIC COMBINATORICS

no. 4

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 ∑ μ≤λ 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) .

Received:
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Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.45
Classification: 05E05,  20F55
Keywords: K-theoretic k-Schur functions, Pieri rule, Coxeter groups, affine symmetric groups 
@article{ALCO_2019__2_4_447_0,
     author = {Takigiku, Motoki},
     title = {A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions},
     journal = {Algebraic Combinatorics},
     pages = {447--480},
     publisher = {MathOA foundation},
     volume = {2},
     number = {4},
     year = {2019},
     doi = {10.5802/alco.45},
     mrnumber = {3997506},
     zbl = {1421.05096},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.45/}
}
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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