Regular characters of GLn(O) and Weil representations over finite fields

In this paper, we will point out a gap in the proof of a theorem in [7] and will give new arguments to give a remedy in the non-dyadic case modulo a conjecture on the triviality of certain Schur multiplier associated with a symplectic space over finite field. The new argument uses the Schrodinger representation of the Heisenberg group associated with a symplectic space over a finite field, and a simple application of Weil representation. This argument is applicable to the regular characters in general which include the cuspidal cases as well as the regular split cases. (C) 2015 Elsevier Inc. All rights reserved.