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 Schrödinger 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.