Automorphic functionals for the minimal representations of groups of type $D_n$ and $E_n$

Nadya Gurevich; David Kazhdan

Automorphic functionals for the minimal representations of groups of type $D_n$ and $E_n$

Representation Theory 2025-02-18 v3

Authors: Nadya Gurevich , David Kazhdan

Abstract

Let $G$ be a split simply-connected group of type $D$ or $E$ . The minimal automorphic representation $\Pi$ of $G(\mathbb A)$ admits a realization on a space of functions $\mathcal S(X(\mathbb A))$ for a variety $X$ . In this paper we write explicitly an automorphic, i.e. $G(F)$ -invariant, functional on $\mathcal S(X(\mathbb A)).$

Keywords

automorphic functionals minimal representations split simply-connected groups type D and E groups automorphic representation

Cite

@article{arxiv.2403.19640,
  title  = {Automorphic functionals for the minimal representations of groups of type $D_n$ and $E_n$},
  author = {Nadya Gurevich and David Kazhdan},
  journal= {arXiv preprint arXiv:2403.19640},
  year   = {2025}
}

Comments

The introduction and section 3 have been rewritten. The results are mainly unchanged

Automorphic functionals for the minimal representations of groups of type $D_n$ and $E_n$

Abstract

Keywords

Cite

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