CAPELLI-TYPE IDENTITIES AND b-FUNCTIONS OF PREHOMOGENEOUS VECTOR SPACES ASSOCIATED WITH SUB-HANKEL DETERMINANTS

Abstract

We give an explicit formula for Capelli-type identities of prehomogeneous vector spaces associated with sub-Hankel determinants. Moreover, we determine multivariate b-functions of these prehomogeneous vector spaces explicitly. As an application, we solve a conjecture on a b-function raised by Ishi and Kogiso (Seminar on Mathematical Sciences, 39. Keio University, 2016, pp. 83–93) affirmatively.