The smoothness of convolutions of singular orbital measures on complex grassmannians

Sanjiv Kumar Gupta, Kathryn E. Hare*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

It is well known that if G/K is any irreducible symmetric space and μa is a continuous orbital measure supported on the double coset KaK, then the convolution product, μk a, is absolutely continuous for some suitably large k ≤ dimG/K. The minimal value of k is known in some symmetric spaces and in the special case of compact groups or rank one compact symmetric spaces it has even been shown that μk a belongs to the smaller space L2 for some k . Here we prove that this L2 property holds for all the compact, complex Grassmannian symmetric spaces, SU(p + q)/S(U(p) × U(q)) . Moreover, for the orbital measures at a dense set of points a, we prove that μ2 a ϵ L2 (or μ3 a ϵ L2 if p = q ).

Original languageEnglish
Pages (from-to)335-349
Number of pages15
JournalJournal of Lie Theory
Volume31
Issue number2
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • Absolute continuity
  • Complex Grassmannian symmetric space
  • Orbital measure
  • Spherical functions

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this