Principal GL(n)-bundles **are** equivalent to locally free sheaves of rank n, but not in the way you're describing. The easiest way to see this is to note that principal G-bundles have fibers that look like G (in the case of GL(n), these would be n²-dimensional), but locally free sheaves of rank n have n-dimensional fibers. The way you get a locally free sheaf of rank n from a GL(n)-torsor P is by twisting the trivial rank n bundle O<sup>n</sup> (which has a natural GL(n)-action) by the torsor. Explicitly, the locally free sheaf is F=O<sup>n</sup>x<sup>GL(n)</sup>P, whose (scheme-theoretic) points are (v,p), where v is a point of the trivial bundle and p is a point of P, subject to the relation that (v⋅g,p)∼(v,g⋅p). It happens that the map is bijective. Given a locally free sheaf F of rank n, the automorphism sheaf Aut(F) is a GL(n) torsor (and this procedure is inverse to the one I described). Similarly, if you have a group G **and a representation** V, then you can associate to any G-torsor a locally free sheaf of rank dim(V). I don't know of a characterization of which locally free sheaves of rank dim(V) arise in this way. Operations with the locally free sheaf (like taking top exterior power) should just correspond to doing that operation with the representation V, so I think you're right that in the case of SL(n) you get exactly those locally free sheaves whose top exterior power is trivial (since SL(n) has no non-trivial 1-dimensional representations).