#####
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 *R*_{t} denotes the partition
(*t*^{k+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.

The following versions are available: