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Metaplectic covers of $G L_{n}$ and the Gauss-Schering lemma

Richard Hill (2001)

Journal de théorie des nombres de Bordeaux

The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a $2$ -cocycle corresponding to a higher metaplectic extension of GL $_{n} / k$ for any global field $k$ . In the case that $k$ has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...

Metaplektische Erweiterungen von Quaternionenschiefkörpern.

Joachim Klose (1986)

Mathematische Zeitschrift

Micro-Local Analysis of Prehomogeneous Vector Spaces.

M. Kashiwara, M. Sato, T. Kimura (1980/1981)

Inventiones mathematicae

Minimal set of generators of symplectic groups over finite fields

Hiroyuki Ishibashi (1980)

Czechoslovak Mathematical Journal

Minimal Singularities in GLn.

Hanspeter Kraft, Claudio Procesi (1980/1981)

Inventiones mathematicae

Minkowskische Reduktionstheorie über Funktionenkörpern.

G. HARDER (1969)

Inventiones mathematicae

Möbius inversion for the Bruhat ordering on a Weyl group

Daya-Nand Verma (1971)

Annales scientifiques de l'École Normale Supérieure

Modular Harish-Chandra theory. I.

Richard Dipper, Peter Fleischmann (1992)

Mathematische Zeitschrift

Moduli of unipotent representations I: foundational topics

Ishai Dan-Cohen (2012)

Annales de l’institut Fourier

With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let $G$ be such a group. The stack $ℳ_{n} (G)$ of all representations of dimension $n$ is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack $ℳ_{n}^{nd} (G)$ which is better behaved, and, in particular, admits a coarse algebraic space, which...