Convolution of orbital measures on complex grassmannians

Mahmoud Al-Hashami, Boudjemâa Anchouche

Research output: Contribution to journalArticle

Abstract

In [2] and [1], the regularity of the Radon-Nikodym derivative of the convolutions of orbital measures on a compact symmetric space of rank one was studied. The aim of this paper is to extend the results obtained in [1] to the case of complex Grassmannians. More precisely, let M = U/K , where U = SU(p + q) and K = S(U(p)× U(q)), be the complex Grassmannian of a p-plane in Cp+q , p ? q ? 2, a1, ..., ar be r points in U , and consider the convolution product ?a 1 ? ... ? ?ar of the orbital measures ?a1 , ..., ?ar supported on Ka1K, ..., KarK . By a result of Ragozin [10], if r ? dim M, then ?a 1 ? ... ? ?ar is absolutely continuous with respect to the Haar measure of U . The aim of this paper is to investigate the Ck?regularity of the Radon-Nikodym derivative of ?a 1 ? ... ? ?ar with respect to the Haar measure of U . Mathematics Subject Classification 2010: Primary 43A77, 43A90; Secondary 53C35, 28C10.

Original languageEnglish
Pages (from-to)695-713
Number of pages19
JournalJournal of Lie Theory
Volume21
Issue number3
Publication statusPublished - Jan 1 2018

Keywords

  • Convolution of orbital measures
  • Grassmannians
  • Radon-Nikodym derivative
  • Spherical functions

ASJC Scopus subject areas

  • Algebra and Number Theory

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