The Subregular Germ of Orbital Integrals

Download or read book The Subregular Germ of Orbital Integrals written by Thomas Callister Hales and published by American Mathematical Soc.. This book was released on 1992 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integral formula for the subregular germ of a [italic small capital]K-orbital integral is developed. The formula holds for any reductive group over a [italic]p-adic field of characteristic zero. This expression of the subregular germ is obtained by applying Igusa's theory of asymptotic expansions. The integral formula is applied to the question of the transfer of a [italic small capital]K-orbital integral to an endoscopic group. It is shown that the quadratic characters arising in the subregular germs are compatible with the transfer. Details of the transfer are given for the subregular germ of unitary groups.