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

页码：279 / 290

页数：12

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