Séminaire Lotharingien de Combinatoire, 78B.59 (2017), 12 pp.
Motoki Takigiku
On Some Factorization Formulas of K-k-Schur Functions
Abstract.
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.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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