Speaker : Masao Ishikawa (Tottori University, Japan)
Place : Class room : E6 #1409
Time : 10:30 AM ~ 12:00 PM

Title : An Identity for Compound Determinant and its Application

abstract:

In this talk we give a formula for a compound determinant
and use it to derive a Schur function identity.
This compound determinant is a variant of Sylvester's determinant
whose row is parametrized by $n$-element subsets of $\{1,2,\dots,s+n-1\}$
and column is parametrized by compositions of $n$ with at most $s$ parts.
We introduce a partial order on the set of compositions of $n$ with at most $s$ parts,
and use this partial order to compute the determinant.
This determinant identity has an application to compute a determinant
whose entries are certain Schur functions, and this result generalize
a Schur function identity obtained in the paper
"A determinant formula for a holonomic $q$-difference system
associated with Jackson integrals of type $BC_n$" by
K. Aomoto and M. Ito.