An Application of Cauchy-Sylvester's Theorem on Compound Determinants to a BC n-Type Jackson Integral
An Application of Cauchy-Sylvester's Theorem on Compound Determinants to a BC n-Type Jackson Integral
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复合行列式柯西-西尔维斯特定理在BC n型杰克逊积分中的应用
DOI：
10.1007/978-1-4614-0028-8_10
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Masahiko Ito
中科院分区：
文献类型：
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作者：
Masahiko Ito
一个由多重rψ 2r基超几何级数形成的行列式被计算为q-函数的乘积。本文作为复合行列式上Cauchy-Sylvester定理的一个应用给出了它的简单而直接的证明，这也为[M]中给出的经典群特征的行列式公式提供了一个非常简单的证明。李建军，李建军，李建军，等。一类典型群的Weyl - s公式的推广，数学学报（2006），817-825。
A determinant formed by multiple2rψ2rbasic hypergeometric series is evaluated as a product ofq-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].