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 .
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Accepted:
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DOI: 10.5802/alco.45
Keywords: $K$-theoretic $k$-Schur functions, Pieri rule, Coxeter groups, affine symmetric groups
Takigiku, Motoki 1
@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}, zbl = {1421.05096}, mrnumber = {3997506}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.45/} }
TY - JOUR AU - Takigiku, Motoki TI - A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions JO - Algebraic Combinatorics PY - 2019 SP - 447 EP - 480 VL - 2 IS - 4 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.45/ DO - 10.5802/alco.45 LA - en ID - ALCO_2019__2_4_447_0 ER -
%0 Journal Article %A Takigiku, Motoki %T A Pieri formula and a factorization formula for sums of $K$-theoretic $k$-Schur functions %J Algebraic Combinatorics %D 2019 %P 447-480 %V 2 %N 4 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.45/ %R 10.5802/alco.45 %G en %F 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/articles/10.5802/alco.45/
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