Abstract
I. M. Gel’fand and his collaborators created the theory of general hypergeometric functions (multivariate hypergeometric functions on lattices and hypergeometric functions on Grassmannians). These functions are multivariate generalizations of hypergeometric functions of one variable. They are solutions of certain systems of differential equations (general hypergeometric systems) and are related to the Radon transform. At the present time, a deep connection of these hypergeometric functions with representations of groups is absent. But it is clear that this connection exists. Remark that the theory of q-analogues of Grassmannians and of related generalizations of Gel’fand hypergeometric functions is under elaboration (see, for example, [432]).
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© 1995 Springer Science+Business Media Dordrecht
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Vilenkin, N.J., Klimyk, A.U. (1995). Gel’fand Hypergeometric Functions. In: Representation of Lie Groups and Special Functions. Mathematics and Its Applications, vol 316. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2885-0_6
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DOI: https://doi.org/10.1007/978-94-017-2885-0_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4486-0
Online ISBN: 978-94-017-2885-0
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