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The symmetrized bidisc ${\textbf{G}}_{2}$ is defined by$${\textbf{G}}_{2}:=\{(z_1+z_2,z_1z_2)\in\mathbb{C}^2: |z_1|<1,|z_2|<1,\;z_1,z_2\in\mathbb{C}\}.$$ It is a bounded inhomogeneous pseudoconvex domainwithout $\mathcal{C}^1$ boundary, and especially the symmetrized bidisc hasn'tany strongly pseudoconvex boundary point and the boundary behavior of bothCarath\'eodory and Kobayashi metrics over the symmetrized bidisc is hard todescribe precisely. In this paper, we study the boundary Schwarz lemma forholomorphic self-mappings of the symmetrized bidisc ${\textbf{G}}_2$, and ourboundary Schwarz lemma in the paper differs greatly from the earlier relatedresults.

The Schwarz Lemma at the Boundary of the Symmetrized Bidisc