Construction and classification of systems of multi-variable commutative differential operators

点击翻译按钮获取中文摘要

We studied several topics related to the systems of commutative differential operators. Obtained results are as follows :(1) The arrangement of singular lines of a pair of commutative differential operators of rank two with an inverse square potential function is determined by the stationary points of the potential function of BC-type Sutherland model.(2) The explicit formula of the discrete series Whittaker functions on Spin(2n,2).(3) The standard Whittaker (g,K)-modules are defined. Their structures are determined when (i) the infinitesimal character is generic, and (ii) the group is U(n,1) and the infinitesimal character is integral.(4) Three-term relations between interpolation polynomials for a BC_n-type hypergeometric series.