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The Picard group of the moduli of Gbundles on a curve
 Compositio Math. 112
, 1998
"... This paper is concerned with the moduli space of principal Gbundles on an algebraic curve, for G a complex semisimple group. While the case G = SLr, which corresponds to vector bundles, has been extensively studied in algebraic geometry, the general case has attracted much less attention until rec ..."
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Cited by 33 (3 self)
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This paper is concerned with the moduli space of principal Gbundles on an algebraic curve, for G a complex semisimple group. While the case G = SLr, which corresponds to vector bundles, has been extensively studied in algebraic geometry, the general case has attracted much less attention until recently, when it
Moduli of metaplectic bundles on curves and Thetasheaves
, 2004
"... We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program. For a smooth projective curve X we introduce an algebraic stack ˜ BunG of metaplectic bundles on X. It also has a local version ˜ GrG, which is a ge ..."
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Cited by 23 (9 self)
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We give a geometric interpretation of the Weil representation of the metaplectic group, placing it in the framework of the geometric Langlands program. For a smooth projective curve X we introduce an algebraic stack ˜ BunG of metaplectic bundles on X. It also has a local version ˜ GrG, which is a gerbe over the affine grassmanian of G. We define a categorical version of the (nonramified) Hecke algebra of the metaplectic group. This is a category Sph ( ˜ GrG) of certain perverse sheaves on ˜ GrG, which act on ˜ BunG by Hecke operators. A version of the Satake equivalence is proved describing Sph ( ˜ GrG) as a tensor category. Further, we construct a perverse sheaf on ˜ BunG corresponding to the Weil representation and show that it is a Hecke eigensheaf with respect to Sph ( ˜ GrG).
The Line Bundles on Moduli Stacks of Principal Bundles on a Curve
 DOCUMENTA MATH.
, 2010
"... Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G–bundles on any smooth projective curve over k. ..."
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Cited by 9 (5 self)
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Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G–bundles on any smooth projective curve over k.
Contents
, 1999
"... 2. Generalities on principal Gbundles 6 3. Algebraic stacks 8 ..."
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Sergey Lysenko
, 2004
"... Historically θseries have been one of the major methods of constructing automorphic forms. A representationtheoretic appoach to the theory of θseries, as discoved by A. Weil [18] and extended by R. Howe [12], is based on the oscillator representation of the metaplectic group (cf. [17] for a recen ..."
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Historically θseries have been one of the major methods of constructing automorphic forms. A representationtheoretic appoach to the theory of θseries, as discoved by A. Weil [18] and extended by R. Howe [12], is based on the oscillator representation of the metaplectic group (cf. [17] for a recent survey). In this paper we propose a geometric interpretation this representation