Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Symmetries of the hypergeometric function $\phantom {}_mF_{m-1}$
HTML articles powered by AMS MathViewer

by Oleg Gleizer PDF
Trans. Amer. Math. Soc. 360 (2008), 2547-2580 Request permission

Abstract:

In this paper, we show that the generalized hypergeometric function $\phantom {}_mF_{m-1}$ has a one parameter group of local symmetries, which is a conjugation of a flow of a rational Calogero-Mozer system. We use the symmetry to construct fermionic fields on a complex torus, which have linear-algebraic properties similar to those of the local solutions of the generalized hypergeometric equation. The fields admit a nontrivial action of the quaternions based on the above symmetry. We use the similarity between the linear-algebraic structures to introduce the quaternionic action on the direct sum of the space of solutions of the generalized hypergeometric equation and its dual. As a side product, we construct a “good” basis for the monodromy operators of the generalized hypergeometric equation inspired by the study of multiple flag varieties with finitely many orbits of the diagonal action of the general linear group by Magyar, Weyman, and Zelevinsky. As an example of computational effectiveness of the basis, we give a proof of the existence of the monodromy invariant hermitian form on the space of solutions of the generalized hypergeometric equation (in the case of real local exponents) different from the proofs of Beukers and Heckman and of Haraoka. As another side product, we prove an elliptic generalization of Cauchy identity.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 33C20
  • Retrieve articles in all journals with MSC (2000): 33C20
Additional Information
  • Oleg Gleizer
  • Affiliation: Apartment 302, 309 S. Sherbourne Drive, Los Angeles, California 90048
  • Email: ogleizer@mac.com
  • Received by editor(s): March 21, 2005
  • Received by editor(s) in revised form: February 20, 2006
  • Published electronically: November 28, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2547-2580
  • MSC (2000): Primary 33C20
  • DOI: https://doi.org/10.1090/S0002-9947-07-04369-3
  • MathSciNet review: 2373325