A domain in $\mathbb C^4$ and its connection with $\mu$-synthesis problem

Sourav Pal; Nitin Tomar

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arXiv · 2603.01483

A domain in $\mathbb C^4$ and its connection with $\mu$-synthesis problem

Sourav Pal·Nitin Tomar

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Abstract

We explore a domain $\mathbb F$ in $\mathbb C^4$ that has structural similarities with the hexablock $\mathbb{H} \subset \mathbb C^4$. It leads to the question if these two domains are biholomorphic. In this paper, we answer this question in negative. We provide alternative characterizations of the domain $\mathbb{F}$ and find its connection with the domains associated with $\mu$-synthesis problem such as the symmetrized bidisc, the tetrablock, the pentablock and the hexablock. We also address the following question: does $\mathbb{F}$ (which is biholomorphic with $\mathbb L_4$) arise from a $\mu$-synthesis problem in the same manner as $\mathbb{G}_2$ and $\mathbb{E}$ ?

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Sourav Pal, Nitin Tomar. 2026-03-02. A domain in $\mathbb C^4$ and its connection with $\mu$-synthesis problem. https://arxiv.org/abs/2603.01483

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