2015/03/18 by Koyama, Tamio
#16S32 #33E20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1503.05261
In this paper, we discuss a system of differential equations for the Fisher integral on the special orthogonal group. Especially, we explicitly give a set of linear differential operators which generates the annihilating ideal of the Fisher integral, and we prove that the annihilating ideal is a maximal left ideal of the ring of differential operators with polynomial coefficients. Our proof is given by a discussion concerned with an annihilating ideal of a Schwartz distribution associated with the Haar measure on the special orthogonal group. We also give differential operators annihilating the Fisher integral for the diagonal matrix by a new approach.