KIRILLOV-FRENKEL CHARACTER FORMULA FOR LOOP GROUPS, RADIAL PART AND BROWNIAN SHEET

被引：3

作者：

Defosseux, Manon ^{[1
]}

机构：

[1] Univ Paris 05, Lab Mat Appl Paris 5, 45 Rue St Peres, F-75270 Paris 06, France

来源：

ANNALS OF PROBABILITY | 2019年 / 47卷 / 02期

关键词：

Kirillov character formula; loop group; Brownian sheet; radial part; Doob transform; Brownian motion in affine Weyl chamber; QUASI-INVARIANCE; MOTION;

D O I：

10.1214/18-AOP1278

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the coadjoint action of a Loop group of a compact group on the dual of the corresponding centrally extended Loop algebra and prove that a Brownian motion in a Cartan subalgebra conditioned to remain in an affine Weyl chamber-which can be seen as a space time conditioned Brownian motion-is distributed as the radial part process of a Brownian sheet on the underlying Lie algebra.

引用

页码：1036 / 1055

页数：20