The automorphism group of the tetrablock

Abstract

The tetrablock is a domain in 3-dimensional complex space that meets 3-dimensional Euclidean space in a regular tetrahedron. It is shown to be inhomogeneous and its automorphism group is determined. A type of Schwarz lemma for the tetrablock is proved. The action of the automorphism group is described in terms of a certain natural foliation of the tetrablock by complex geodesic discs.

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References in corpus (1)

• A Schwarz lemma for a domain related to mu-synthesis

Cited by in corpus (12)

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• Toeplitz operators on the weighted Bergman spaces of quotient domains
• A Schwarz lemma for a domain related to mu-synthesis
• The weighted Bergman spaces and complex reflection groups
• Geometric properties of domains related to $\mu$-synthesis
• Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock
• The group of automorphisms of the pentablock
• The Lempert theorem and the tetrablock