  We introduce a conjecture on Virasoro constraints for the moduli space of
stable sheaves on a smooth projective surface. These generalise the Virasoro
constraints on the Hilbert scheme of a surface found by Moreira
(arXiv:2008.13746) and Moreira, Oblomkov, Okounkov and Pandharipande
(arXiv:2008.12514). We verify the conjecture in many nontrivial cases by using
a combinatorial description of equivariant sheaves found by Klyachko.
