On the integrability of a representation of sl(2, R)

被引：10
作者：
Ben Said, Salem [1 ]
机构：
[1] Univ Nancy 1, Dept Math, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2007年 / 250卷 / 02期
关键词：
Dunkl operators; integrable representations; Schrodinger model; Dunkl transform; Bochner identity;
D O I：
10.1016/j.jfa.2007.04.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Dunkl operators involve a multiplicity function k as parameter [C.F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989) 167-183]. For positive real values of this function, we consider on the Schwartz space S(R-N) a representation omega(k) of sl(2, R) defined in terms of the Dunkl-Laplacian operator. By means of a beautiful theorem due to E. Nelson, we prove that w(k) exponentiates to a unique unitary representation of the universal covering group of SL(2, R). The representation theory is used to derive an identity of Bochner type for the Dunkl transform. (C) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：249 / 264
页数：16
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