English

Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument

Algebraic Geometry 2025-05-27 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.2005.06162,
  title  = {Algebraic Analysis of the Hypergeometric Function 1F1 of a Matrix Argument},
  author = {Paul Görlach and Christian Lehn and Anna-Laura Sattelberger},
  journal= {arXiv preprint arXiv:2005.06162},
  year   = {2025}
}

Comments

26 pages. v2 changes: included Appendix discussing the singular locus for degenerate parameters

R2 v1 2026-06-23T15:30:25.730Z