非对称差分Whittaker函数
Nonsymmetric difference Whittaker functions
摘要：
从非对称整体差分球函数出发，定义并计算了任意约化根系的旋量（非对称）整体q-Whittaker函数，它们是Nil-DAHA的DAHA-傅里叶变换的再生核，也是q-Toda-Dunkl本征值问题的解.我们引入旋量q-Toda-Dunkl算子作为DAHA理论中差分Dunkl算子在旋量变体Ruijsenaars方法下的极限。它们的一般代数理论（任何约化的根系）是本文的核心部分，基于W-旋量的新技术和仿射根系的组合学的相应发展。
英文摘要：
Starting with nonsymmetric global difference spherical functions, we define and calculate spinor (nonsymmetric) global q-Whittaker functions for arbitrary reduced root systems, which are reproducing kernels of the DAHA-Fourier transforms of Nil-DAHA and solutions of the q-Toda-Dunkl eigenvalue problem. We introduce the spinor q-Toda-Dunkl operators as limits of the difference Dunkl operators in DAHA theory under the spinor variant of the Ruijsenaars procedure. Their general algebraic theory (any reduced root systems) is the key part of this paper, based on the new technique of W-spinors and corresponding developments in combinatorics of affine root systems.
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