Small automorphic representations and degenerate Whittaker vectors

@article{Gustafsson2014SmallAR,
  title={Small automorphic representations and degenerate Whittaker vectors},
  author={H. Gustafsson and A. Kleinschmidt and D. Persson},
  journal={arXiv: Number Theory},
  year={2014}
}
  • 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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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 63 REFERENCES
    On Certain L-Functions
    • 427
    • PDF
    Nilpotent orbits in semisimple Lie algebras
    • 826
    • Highly Influential
    Finite groups of Lie type
    • 593
    • Highly Influential
    The Multiplicity One Theorem for GL n
    • 373
    Automorphic Forms and Representations
    • 690
    • PDF
    Conformal and Quasiconformal Realizations¶of Exceptional Lie Groups
    • 149
    • PDF
    The unramified principal series of $p$-adic groups. II. The Whittaker function
    • 305
    • Highly Influential
    • PDF
    Minimal Representations, Spherical Vectors¶and Exceptional Theta Series
    • 71
    • Highly Influential
    • PDF
    Multiplicity one Theorems
    • 158
    • PDF