Rayleigh triangles and non-matrix interpolation of matrix beta integrals
Rayleigh triangles and non-matrix interpolation of matrix beta integrals
复制标题
瑞利三角形和矩阵 beta 积分的非矩阵插值
DOI：
10.4213/sm727
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发表时间：
2003
影响因子：
0.8
通讯作者：
Y. Neretin
中科院分区：
文献类型：
--
作者：
Y. Neretin
大小为n的瑞利三角形是n(n+1)/2个实数{lambda}{sub kl}的集合，其中1{<=}l{<=}k{<=}n，对于固定k，它们随着k的增加而减小，对于固定k-l，它们随着k的增加而增大。我们在瑞利三角形的空间上构造了一个β积分族，它插入了西格尔、华卢京和金迪金类型的矩阵积分，与地面场的维度（R、C或四元数H）有关。我们还在对称空间U(n)、U(n)/O(n)、U(2n)/Sp(n)的逆极限上插值了Hua-Pickrell测度。我们的积分族还包括塞尔伯格积分。
A Rayleigh triangle of size n is a set of n(n+1)/2 real numbers {lambda}{sub kl}, where 1{<=}l{<=}k{<=}n, which are decreasing as k increases for fixed k and are increasing as k increases for fixed k-l. We construct a family of beta integrals over the space of Rayleigh triangles which interpolate matrix integrals of the types of Siegel, Hua Loo Keng, and Gindikin with respect to the dimension of the ground field (R, C, or the quaternions H). We also interpolate the Hua-Pickrell measures on the inverse limits of the symmetric spaces U(n), U(n)/O(n), U(2n)/Sp(n). Our family of integrals also includes the Selberg integral.