Introduction to Automorphic Forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$

Jae-Hyun Yang

Introduction to Automorphic Forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$

Number Theory 2024-01-24 v2

Authors: Jae-Hyun Yang

Abstract

In this paper, we introduce the notion of automorphic forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$ and discuss invariant differential operators on the Minkowski-Euclid space. The group $GL{n,\BR}\ltimes \BR^{(m,n)}$ is the semidirect product of $GL(n,\BR)$ and the additive group $\BR^{(m,n)}$ and is {\it not} a reductive group. The Minkowski-Euclid space is the quotient space of $GL(n,\BR)\ltimes \BR^{(m,n)}$ by $O(n,\BR)$ . The Minkowski-Euclid space is an important non-symmetric homogeneous space geometrically and number theoretically. We present some open problems to be solved in the future.

Cite

@article{arxiv.2312.02794,
  title  = {Introduction to Automorphic Forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$},
  author = {Jae-Hyun Yang},
  journal= {arXiv preprint arXiv:2312.02794},
  year   = {2024}
}

Comments

29 pages. arXiv admin note: text overlap with arXiv:1910.06246, arXiv:1706.07177 In the introduction, I explained how the action (1.2) arises. I added three more references

Introduction to Automorphic Forms for $GL(n,\BZ)\ltimes \BZ^{(m,n)}$

Abstract

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