Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument
arXiv:2005.06162 · doi:10.1007/s13366-020-00546-z
Abstract
In this article, we investigate Muirhead's classical system of differential operators for the hypergeometric function 1F1 of a matrix argument. We formulate a conjecture for the combinatorial structure of the characteristic variety of its Weyl closure which is both supported by computational evidence as well as theoretical considerations. In particular, we determine the singular locus of this system.
26 pages. v2 changes: included Appendix discussing the singular locus for degenerate parameters