We prove a myriad of results related to the stabilizer in an algebraic group G generic vector representation V over algebraically closed field k. Our are on level schemes, which carries more information than considering both Lie algebra and G(k) k-points. For simple faithful irreducible, we existence general position, sometimes called principal orbit type. determine those for position is smooth...

Bell inequality with self-testing property has played an important role in quantum information field both fundamental and practical applications. However, it is generally challenging to find inequalities for multipartite states actually there are not many known candidates. In this work, we propose a systematical framework construct from stabilizers which maximally violated by general stabilizer...

Culler's theorem states that for a finitely generated free group F, of rank at least 2, any finite subgroup of Out(F) fixes a point in Outer Space. This theorem is comparable to Nieslen Realization: for a closed surface with negative Euler characteristic, any finite subgroup of the mapping class group fixes a point in the Teichmüller sapce for the surface as proved by Kerckhoff. For nonnegative...