Harish-Chandra's Ξ function
In mathematical harmonic analysis, Harish-Chandra's Ξ function is a special spherical function on a semisimple Lie group, studied by.
Harish-Chandra used it to define Harish-Chandra's Schwartz space.
gives a detailed description of the properties of Ξ.
Definition
where- 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 is the element a in the Iwasawa decomposition g=''nak''