Harish-Chandra c-function

E876151

analytic function object in representation theory

The Harish-Chandra c-function is a key analytic function in representation theory and harmonic analysis on semisimple Lie groups, encoding the Plancherel measure and asymptotic behavior of spherical functions.

Try in SPARQL Jump to: Statements Referenced by

Statements (43)

Predicate	Object
instanceOf	analytic function ⓘ object in representation theory ⓘ
appearsIn	Harish-Chandra Plancherel formula NERFINISHED ⓘ Harish-Chandra’s work on the Plancherel formula ⓘ harmonic analysis on semisimple Lie groups and symmetric spaces literature ⓘ inversion formula for the spherical Fourier transform ⓘ
associatedWith	Cartan decomposition of a semisimple Lie group NERFINISHED ⓘ Iwasawa decomposition of a semisimple Lie group NERFINISHED ⓘ minimal parabolic subgroup ⓘ principal series representations ⓘ
dependsOn	multiplicities of restricted roots ⓘ root system of the Lie algebra ⓘ
domain	complexified dual of a Cartan subalgebra ⓘ
encodes	Plancherel measure for semisimple Lie groups ⓘ asymptotic behavior of spherical functions ⓘ
field	harmonic analysis ⓘ representation theory ⓘ theory of semisimple Lie groups ⓘ
generalizationOf	Gamma function factors in rank-one cases ⓘ
hasRankOneForm	ratio of Gamma functions ⓘ
influenced	later developments in non-compact harmonic analysis ⓘ
namedAfter	Harish-Chandra NERFINISHED ⓘ
property	Weyl group invariant up to explicit factors ⓘ meromorphic in the spectral parameter ⓘ
relatedTo	Harish-Chandra isomorphism NERFINISHED ⓘ Plancherel theorem for semisimple Lie groups NERFINISHED ⓘ c-function of Heckman–Opdam theory ⓘ spherical Fourier transform ⓘ spherical functions ⓘ zonal spherical functions ⓘ
role	density factor in the Plancherel measure ⓘ normalizing factor for intertwining operators ⓘ normalizing factor for spherical functions ⓘ
satisfies	functional equations under Weyl group action ⓘ
specialCaseOf	Gindikin–Karpelevich c-function in p-adic theory NERFINISHED ⓘ
usedIn	decomposition of the regular representation ⓘ harmonic analysis on Riemannian symmetric spaces ⓘ harmonic analysis on real reductive groups ⓘ spectral decomposition of L^2(G/K) ⓘ
usedToCompute	L^2-norms of spherical functions ⓘ
usedToDefine	Plancherel density on the unitary dual ⓘ
usedToStudy	tempered representations of semisimple Lie groups ⓘ unitary principal series ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Harish → notableFor → Harish-Chandra c-function ⓘ

subject surface form: Harish-Chandra

Plancherel theorem for real reductive groups → involves → Harish-Chandra c-function ⓘ