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Geometrizing the minimal representations of even orthogonal groups
- Source :
- Represent. Theory 17 (2013), 263-325
- Publication Year :
- 2011
-
Abstract
- Let X be a smooth projective curve. Write Bun_{SO_{2n}} for the moduli stack of SO_{2n}-torsors on X. We give a geometric interpretation of the automorphic function f on Bun_{SO_{2n}} corresponding to the minimal representation. Namely, we construct a perverse sheaf K on Bun_{SO_{2n}} such that f should be equal to the trace of Frobenius of K plus some constant function. We also calculate K explicitely for curves of genus zero and one. The construction of K is based on some explicit geometric formulas for the Fourier coefficients of f 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.<br />Comment: LaTeX2e, 69 pages, final version, to appear in Representation theory (electronic J. of AMS)
Details
- Database :
- arXiv
- Journal :
- Represent. Theory 17 (2013), 263-325
- Publication Type :
- Report
- Accession number :
- edsarx.1101.1408
- Document Type :
- Working Paper