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arXiv · 1510.04377

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

Koichi Takase
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Abstract

In this paper, we will point out a gap in the proof of a theorem of G.Hill (J. Algebra, 174 (1995), 610-635) 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.

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Koichi Takase. 2015-10-15. Regular characters of $GL_n(O)$ and Weil representations over finite fields. https://arxiv.org/abs/1510.04377

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