Harish-Chandra's Ξ function

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematical harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group, studied by Harish-Chandra (1966, section 16).

Harish-Chandra used it to define Harish-Chandra's Schwartz space.

Wallach (1988, 4.5) gives a detailed description of the properties of Ξ.



  • K is a maximal compact subgroup of a semisimple Lie group with Iwasawa decomposition G=NAK
  • g is an element of G
  • ρ is a Weyl vector
  • a(g) is the element a in the Iwasawa decomposition g=nak