Corpus ID: 119625589

Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$

@article{Ahlen2017FourierCA,
  title={Fourier coefficients attached to small automorphic representations of \$\{\mathrm\{SL\}\}_n(\mathbb\{A\})\$},
  author={O. Ahl'en and H. Gustafsson and A. Kleinschmidt and B. Liu and D. Persson},
  journal={arXiv: Representation Theory},
  year={2017}
}
  • O. Ahl'en, H. Gustafsson, +2 authors D. Persson
  • Published 2017
  • Mathematics, Physics
  • arXiv: Representation Theory
  • We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for… CONTINUE READING

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