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arXiv · 2205.08490

A remark on the existence of equivariant functions

Shingo Sugiyama
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Abstract

Let $\Gamma$ be a Fuchsian group in ${\rm SL}_2(\mathbb{R})$. In this note, we discuss the existence of $\rho$-equivariant functions for a two-dimensional representation $\rho$ of $\Gamma$. This assertion was first stated by Saber and Sebbar in 2020, and this note partially fills a gap of their statement by proving the assertion for a certain class of Fuchsian groups such as conjugates of subgroups of ${\rm SL}_2(\mathbb{Z})$.

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Shingo Sugiyama. 2022-05-17. A remark on the existence of equivariant functions. https://arxiv.org/abs/2205.08490

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