Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$

Abstract

An element of a group is called $\text{strongly reversible}$ or $\text{strongly real}$ if it can be expressed as a product of two involutions. We provide necessary and sufficient conditions for an element of $\mathrm{SL}(n,\mathbb{C})$ to be a product of two involutions. In particular, we classify the strongly reversible conjugacy classes in $\mathrm{SL}(n,\mathbb{C})$.

Final version (26 pages), incorporating revisions to the title, abstract, and statement of the main result from the earlier draft; to appear in the Proceedings of the Edinburgh Mathematical Society