Geometrizing the minimal representations of even orthogonal groups

@article{Lafforgue2011GeometrizingTM,
  title={Geometrizing the minimal representations of even orthogonal groups},
  author={V. Lafforgue and S. Lysenko},
  journal={arXiv: Representation Theory},
  year={2011}
}
  • V. Lafforgue, S. Lysenko
  • Published 2011
  • Mathematics
  • arXiv: Representation Theory
  • 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… CONTINUE READING
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