English

Nonabelian Fourier Kernels on $\mathrm{SL}_2$ and $\mathrm{GL}_2$

Number Theory 2024-09-25 v2 Representation Theory

Abstract

For G=SL2G=\mathrm{SL}_2 or GL2\mathrm{GL}_2, we present explicit formulas for the nonabelian Fourier kernels on GG, as conjectured by A. Braverman and D. Kazhdan. Additionally, we furnish explicit formulas for the orbital Hankel transform on GG, a topic investigated by the second author, and provide an explicit formula for the stable orbital integral of the basic function. These results are applicable to local fields with residual characteristics other than two.

Keywords

Cite

@article{arxiv.2409.14696,
  title  = {Nonabelian Fourier Kernels on $\mathrm{SL}_2$ and $\mathrm{GL}_2$},
  author = {Zhilin Luo and Ngo Bao Chau},
  journal= {arXiv preprint arXiv:2409.14696},
  year   = {2024}
}

Comments

106pp. Any comments are very welcome

R2 v1 2026-06-28T18:53:15.174Z