Small automorphic representations and degenerate Whittaker vectors

  title={Small automorphic representations and degenerate Whittaker vectors},
  author={H. Gustafsson and A. Kleinschmidt and D. Persson},
  journal={arXiv: Number Theory},
  • H. Gustafsson, A. Kleinschmidt, D. Persson
  • Published 2014
  • Mathematics, Physics
  • arXiv: Number Theory
  • We investigate Fourier coefficients of automorphic forms on split simply-laced Lie groups G. We show that for automorphic representations of small Gelfand-Kirillov dimension the Fourier coefficients are completely determined by certain degenerate Whittaker vectors on G. Although we expect our results to hold for arbitrary simply-laced groups, we give complete proofs only for G=SL(3) and G=SL(4). This is based on a method of Ginzburg that associates Fourier coefficients of automorphic forms with… CONTINUE READING

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