Geometrizing the minimal representations of even orthogonal groups

Geometrizing the minimal representations of even orthogonal groups

Let X \mathrm {Bun}_{\mathrm {S}\mathbb{O}_{2n}} \mathrm {S}\mathbb{O}_{2n}. We give a geometric interpretation of the automorphic function f \mathrm {Bun}_{\mathrm {S}\mathbb{O}_{2n}} \mathcal {K}_H \mathrm {Bun}_{\mathrm {S}\mathbb{O}_{2n}} should be equal to the trace of the Frobenius of \mathcal...

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Veröffentlicht in:Representation theory 2013-05, Vol.17 (10), p.263-325
Hauptverfasser: Lafforgue, Vincent, Lysenko, Sergey
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Lysenko, Sergey
description Let X \mathrm {Bun}_{\mathrm {S}\mathbb{O}_{2n}} \mathrm {S}\mathbb{O}_{2n}. We give a geometric interpretation of the automorphic function f \mathrm {Bun}_{\mathrm {S}\mathbb{O}_{2n}} \mathcal {K}_H \mathrm {Bun}_{\mathrm {S}\mathbb{O}_{2n}} should be equal to the trace of the Frobenius of \mathcal {K}_H on one hand, and on the geometric theta-lifting on the other hand. Our construction makes sense for more general simple algebraic groups, we formulate the corresponding conjectures. They could provide a geometric interpretation of some unipotent automorphic representations in the framework of the geometric Langlands program.
doi_str_mv 10.1090/S1088-4165-2013-00431-4
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title Geometrizing the minimal representations of even orthogonal groups
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