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Volume 1, Issue 1

Beta super-functions on super-Grassmannians

Pages: 41 – 60


Mee Seong Im and Michaƚ Zakrzewski


Israel M. Gelfand gave a geometric interpretation for general hypergeometric functions as sections of the tautological bundle over a complex Grassmannian \(G_{k,n}\). In particular, the beta function can be understood in terms of \(G_{2,3}\). In this manuscript, we construct one of the simplest generalizations of the Euler beta function by adding arbitrary many odd variables to the classical setting. We also relate the beta super-function to the gamma and the hypergeometric function.

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Received: 20 April 2019; Accepted: 23 June 2019.