In this note, we construct a birational map of a moduli space of stable sheaves on a $K3$ surface induced by a reflection functor.
"Birational Maps of Moduli Spaces of Vector Bundles on $K3$ Surfaces." Tokyo J. Math. 34 (2) 473 - 491, December 2011. https://doi.org/10.3836/tjm/1327931397