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Geometric construction of metaplectic covers of $GL_{n}$ in characteristic zero | | Richard Hill
; | | Date: |
1 Aug 2007 | | Abstract: | This paper presents a new construction of the m-fold metaplectic cover of
$GL_{n}$ over an algebraic number field k, where k contains a primitive m-th
root of unity. A 2-cocycle on $GL_{n}(A)$ representing this extension is
given and the splitting of the cocycle on $GL_{n}(k)$ is found explicitly. The
cocycle is smooth at almost all places of k. As a consequence, a formula for
the Kubota symbol on $SL_{n}$ is obtained. The construction of the paper
requires neither class field theory nor algebraic K-theory, but relies instead
on naive techniques from the geometry of numbers introduced by W. Habicht and
T. Kubota. The power reciprocity law for a number field is obtained as a
corollary. | | Source: | arXiv, 0708.0108 | | Services: | Forum | Review | PDF | Favorites | |
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