# ALGEBRAIC COMBINATORICS

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

We give a Pieri-type formula for the sum of $K$-$k$-Schur functions ${\sum }_{\mu \le \lambda }{g}_{\mu }^{\left(k\right)}$ over a principal order ideal of the poset of $k$-bounded partitions under the strong Bruhat order, whose sum we denote by ${\stackrel{˜}{g}}_{\lambda }^{\left(k\right)}$. As an application of this, we also give a $k$-rectangle factorization formula ${\stackrel{˜}{g}}_{{R}_{t}\cup \lambda }^{\left(k\right)}={\stackrel{˜}{g}}_{{R}_{t}}^{\left(k\right)}{\stackrel{˜}{g}}_{\lambda }^{\left(k\right)}$ where ${R}_{t}=\left({t}^{k+1-t}\right)$, analogous to that of $k$-Schur functions ${s}_{{R}_{t}\cup \lambda }^{\left(k\right)}={s}_{{R}_{t}}^{\left(k\right)}{s}_{\lambda }^{\left(k\right)}$.

Revised : 2018-10-19
Accepted : 2018-10-28
Published online : 2019-08-01
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},
publisher = {MathOA foundation},
volume = {2},
number = {4},
year = {2019},
pages = {447-480},
doi = {10.5802/alco.45},
language = {en},
url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_4_447_0}
}

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/item/ALCO_2019__2_4_447_0/

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