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

• 成果类型: Article
• 署名作者: Defosseux, Manon
• 署名单位: Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1278
• 发表日期: 2019
• 页码: 1036-1055
• 关键词: quasi-invariance; motion

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.