Formule de Plancherel sur $GL_n \times GL_n \backslash GL_{2n}$

Nicolas Duhamel

Formule de Plancherel sur $GL_n \times GL_n \backslash GL_{2n}$

Representation Theory 2019-12-19 v1

Authors: Nicolas Duhamel

Abstract

Let $F$ be a non archimedian local field and $H_n(F)$ the Shalika subgroup of $GL_{2n}(F)$ . We prove an explicit Plancherel formula for $H_n(F) \backslash GL_{2n}(F)$ using the theory of Jacquet-Shalika of zeta functions and we deduce Plancherel decompositions for $H_n(F) \backslash GL_{2n}(F)$ and $GL_{n}(F) \times GL_{n}(F) \backslash GL_{2n}(F)$ .

Keywords

plancherel formula shalika subgroup local field zeta functions plancherel decomposition reductive groups

Cite

@article{arxiv.1912.08497,
  title  = {Formule de Plancherel sur $GL_n \times GL_n \backslash GL_{2n}$},
  author = {Nicolas Duhamel},
  journal= {arXiv preprint arXiv:1912.08497},
  year   = {2019}
}

Comments

in French

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