On a Conjecture of Braverman and Kazhdan.

This article contains a proof of a conjectural technical lemma of Braverman and Kazhdan in their article gamma-functions of representations and lifting in the special case of general linear groups over finite fields. The lemma implies a number of nice properties of their gamma sheaves, in particular these gamma sheaves are indeed the correct geometrical incarnations of their representation-theoretic gamma-functions. [ABSTRACT FROM AUTHOR]