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Some $ q$-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras


Author: Robert A. Gustafson
Journal: Trans. Amer. Math. Soc. 341 (1994), 69-119
MSC: Primary 33D05; Secondary 17B20, 33C45, 33C80, 33D70, 33D80
DOI: https://doi.org/10.1090/S0002-9947-1994-1139492-3
MathSciNet review: 1139492
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Abstract: Multidimensional generalizations of beta type integrals of Barnes, Ramanujan, Askey-Wilson, and others are evaluated. These integrals are analogues of the summation theorems for multilateral hypergeometric series associated to the simple Lie algebras of classical type and type $ {G_2}$. Many of these integrals can also be written as group integrals over a compact Lie group or conjugation invariant integrals over the corresponding Lie algebra.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1994-1139492-3
Keywords: Multivariate beta integrals, multivariate Mellin-Barnes integrals, $ q$-beta integrals, compact Lie groups, semisimple Lie algebras hypergeometric series very-well-poised on semisimple Lie algebras
Article copyright: © Copyright 1994 American Mathematical Society

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