Title: An Extension of Sato-Kimura Theorem for Semi-invariant rings
Abstract: We prove an analog of a theorem of Sato–Kimura for semi-invariant rings arising from representations of finite-dimensional algebras over an algebraically closed field K of characteristic 0. Assuming the coordinate ring is factorial and the representation variety has generic orbits of codimension one, we show that the semi-invariant ring is a complete intersection and describe the structure of the ring. We also discuss the hereditary case, where these results admit a more explicit interpretation. This is joint work with Charles Paquette and David Wehlau.