On a Classical Limit of q-Deformed Whittaker Functions

被引：15
|
作者：
Gerasimov, Anton [1 ,2 ,3 ]
Lebedev, Dimitri [1 ]
Oblezin, Sergey [1 ]
机构：
[1] Inst Theoret & Expt Phys, Moscow 117259, Russia
[2] Trinity Coll Dublin, Sch Math, Dublin 2, Ireland
[3] Trinity Coll Dublin, Hamilton Math Inst, Dublin 2, Ireland
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2012年 / 100卷 / 03期
基金：
爱尔兰科学基金会;
关键词：
q-deformed Whittaker function; Toda chain; Givental integral representation; Gelfand-Zetlin patterns;
D O I：
10.1007/s11005-012-0545-x
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Previously, we derive a representation of q-deformed g(l+1)-Whittaker function as a sum over Gelfand-Zetlin patterns. This representation provides an analog of the Shintani-Casselman-Shalika formula for q-deformed gl(l+1)-Whittaker functions. In this note, we provide a derivation of the Givental integral representation of the classical gl(l+1)-Whittaker function as a limit q -> 1 of the sum over the Gelfand-Zetlin patterns representation of the q-deformed gl(l+1)-Whittaker function. Thus, Givental representation provides an analog the Shintani-Casselman-Shalika formula for classical Whittaker functions.
引用
收藏
页码：279 / 290
页数：12
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