Path Hypergeometric Functions

Xiaoping Xu ()
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Xiaoping Xu: Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics

Chapter Chapter 15 in Representations of Lie Algebras and Partial Differential Equations, 2017, pp 555-616 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-6391-6_15

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DOI: 10.1007/978-981-10-6391-6_15

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