Gamma factors of certain supercuspidal representations

A -factor defined by the doubling method is calculated for certain supercuspidal representations. The result is a sum over a finite group of Lie type, which may be called a non-abelian Gauss sum. It is the sum of the product of a cuspidal character and an Igusa zeta integral. In some cases, we show that our result agrees with what is expected by the local Langlands conjecture. Received: 11 July 1999 / Accepted: 29 December 1999 / Published online: 28 June 2000