We give a Pieri-type formula for the sum of --Schur functions over a principal order ideal of the poset of -bounded partitions under the strong Bruhat order, whose sum we denote by . As an application of this, we also give a -rectangle factorization formula where , analogous to that of -Schur functions .
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: -theoretic -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/item/ALCO_2019__2_4_447_0/} }
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/item/ALCO_2019__2_4_447_0/
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