Mathematical Sciences: Generalized Selberg-Jack Symmetric Functions and Constant Term Identities

这项数学研究的一个中心目标是使用新发展的特殊函数之间的关系来计算复积分。主要的焦点是著名的Selberg公式，该公式用于对称函数乘以Vandermonde行列式的积分，充当权重。这项工作将继续解决这种封闭形式表达式的可能扩展。将作出初步努力，以建立可选函数与Selberg对称函数之比的公式。预计它们将在锦标赛方面得到明确的给予。此外，还将研究贝塔型分布及其正交多项式。此外，还将寻求提供Zeilberger和Bresourd的Q-Dyson定理的推广的函数的分类。据推测，并不是所有这样的函数最终都是对称的。

A central goal of this mathematical research is the use of newly developed relationships between special functions applied to the evaluation of complex integrals. The primary focus is that of the famous Selberg formula for the integration of symmetric functions multiplied against the Vandermonde determinant, acting as a weight. Work will continue addressing possible extensions of this closed form expression. Initial efforts will be made to establish a formula for the ratios of alternantes to the Selberg symmetric functions. It is expected that they will be given explicitly in terms of tournaments. Work will also be done on beta type distributions and their orthogonal polynomials. In addition, the classification of functions which provide extensions of the q- Dyson theorem of Zeilberger and Bressoud will be sought. It is conjectured that not all such functions will turn out to be symmetric.