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Path Hypergeometric Functions

In: Representations of Lie Algebras and Partial Differential Equations

Author

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  • Xiaoping Xu

    (Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics
    University of Chinese Academy of Sciences, School of Mathematics)

Abstract

We prove that certain variations of the classical Weyl functions are solutions of the Calogero-Sutherland model and its generalizations—the Olshanestsky-Perelomov model in various cases. New multi-variable hypergeometric functions related to the root systems of classical simple Lie algebras are introduced. In particular, those of type A give rise to solutions of the Calogero-Sutherland model and those of type C yield solutions of the Olshanestsky-Perelomov model of type. The differential properties and multi-variable hypergeometric equations for these multi-variable hypergeometric functions are given. The Euler integral representations of the type-A functions are found.

Suggested Citation

  • Xiaoping Xu, 2017. "Path Hypergeometric Functions," Springer Books, in: Representations of Lie Algebras and Partial Differential Equations, chapter 0, pages 555-616, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-6391-6_15
    DOI: 10.1007/978-981-10-6391-6_15
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