Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Harish-Chandra's c-function
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, Harish-Chandra's <i>c</i>-function is a function related to the <a href="/facts/Intertwining_operator/KkIkDwIH">intertwining operator</a> between two <a href="/facts/Principal_series_representation/0kgn94Gr">principal series representations</a>, that appears in the <a href="/facts/Plancherel_measure/Wgq285lJ">Plancherel measure</a> for <a href="/facts/Semisimple_Lie_group/m8jA3Bcf">semisimple Lie groups</a>. <a href="/facts/Harish-Chandra/f9De1zCJ">Harish-Chandra</a> (1958a, 1958b) introduced a special case of it defined in terms of the asymptotic behavior of a <a href="/facts/Zonal_spherical_function/myzsFsrU">zonal spherical function</a> of a <a href="/facts/Lie_group/a9jCQyjF">Lie group</a>, and Harish-Chandra (1970) introduced a more general <i>c</i>-function called Harish-Chandra's (generalized) <i>C</i>-function. <a href="/facts/Simon_Gindikin/gI28cHyj">Gindikin</a> and <a href="/facts/Fridrikh_Israilevich_Karpelevich/3wElRyw2"> Karpelevich</a> (1962, 1969) introduced the Gindikin–Karpelevich formula, a product formula for Harish-Chandra's <i>c</i>-function. </p>