Locally Symmetric Spaces Seminar

An orbit method (or Kirillov method) on compact $p$-adic groups establishes a one-to-one correspondence between irreducible representations and coadjoint orbits of dual blobs. After briefly recalling Howe’s Kirillov theory, we discuss its applications for smooth representations of reductive $p$-adic groups, especially in describing asymptotic behavior of characters, and quantifying tempered representations.