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2017 | OriginalPaper | Chapter

15. Path Hypergeometric Functions

Author : Xiaoping Xu

Published in: Representations of Lie Algebras and Partial Differential Equations

Publisher: Springer Singapore

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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.

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Title: Path Hypergeometric Functions
Author: Xiaoping Xu
Publisher: Springer Singapore
Book: Representations of Lie Algebras and Partial Differential Equations
Print ISBN: 978-981-10-6390-9

Electronic ISBN: 978-981-10-6391-6

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-981-10-6391-6_15

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