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

Takigiku, Motoki

A Pieri formula and a factorization formula for sums of

K

-theoretic

k

-Schur functions

Takigiku, Motoki

Algebraic Combinatorics, Volume 2 (2019) no. 4, p. 447-480

Abstract

We give a Pieri-type formula for the sum of $K$ - $k$ -Schur functions $\sum_{μ \leq λ} g_{μ}^{(k)}$ over a principal order ideal of the poset of $k$ -bounded partitions under the strong Bruhat order, whose sum we denote by ${\tilde{g}}_{λ}^{(k)}$ . As an application of this, we also give a $k$ -rectangle factorization formula ${\tilde{g}}_{R_{t} \cup λ}^{(k)} = {\tilde{g}}_{R_{t}}^{(k)} {\tilde{g}}_{λ}^{(k)}$ where $R_{t} = (t^{k + 1 - t})$ , analogous to that of $k$ -Schur functions $s_{R_{t} \cup λ}^{(k)} = s_{R_{t}}^{(k)} s_{λ}^{(k)}$ .

Received : 2018-05-06
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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