Geodesic
On Some Factorization Formulas of K-k-Schur Functions
Séminaire lotharingien de combinatoire, 78B (2017)

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We give some new formulas about factorizations of K-k-Schur functions g(k)λ, analogous to the k-rectangle factorization formula s(k)Rt u λ = s(k)Rt s(k)λ of k-Schur functions, where λ is any k-bounded partition and Rt denotes the partition (tk+1-t) called a k-rectangle. Although a formula of the same form does not hold for K-k-Schur functions, we can prove that g(k)Rt divides g(k)Rt u λ, and in fact more generally that g(k)P divides g(k)P u λ for any multiple k-rectangles P and any k-bounded partition λ. We give the factorization formula of such g(k)P and explicit formulas for g(k)P u λ / g(k)P in some cases. 

@article{SLC_2017_78B_a58,
     author = {Motoki Takigiku},
     title = {On {Some} {Factorization} {Formulas} of {K-k-Schur} {Functions}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a58/}
}
TY  - JOUR
AU  - Motoki Takigiku
TI  - On Some Factorization Formulas of K-k-Schur Functions
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a58/
ID  - SLC_2017_78B_a58
ER  - 
%0 Journal Article
%A Motoki Takigiku
%T On Some Factorization Formulas of K-k-Schur Functions
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a58/
%F SLC_2017_78B_a58
Motoki Takigiku. On Some Factorization Formulas of K-k-Schur Functions. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a58/