Abstract
A determinant formed by multiple 2r ψ2r basic hypergeometric series is evaluated as a product of q-gamma functions. Its simple and direct proof is presented herein as an application of Cauchy–Sylvester’s theorem on compound determinants, which also provides a very simple proof of determinant formulae for classical group characters given in [M. Ito and K. Koike, A generalization of Weyl’s denominator formulas for the classical groups, J. Algebra 302 (2006), 817–825].
Mathematics Subject Classification: Primary: 15A15, 33D67
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Ito, M., Okada, S. (2012). An Application of Cauchy–Sylvester’s Theorem on Compound Determinants to a BC n -Type Jackson Integral. In: Alladi, K., Garvan, F. (eds) Partitions, q-Series, and Modular Forms. Developments in Mathematics, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0028-8_10
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DOI: https://doi.org/10.1007/978-1-4614-0028-8_10
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