Dimension Vectors of Indecomposable Objects for Nilpotent Operators of Degree 6 with One Invariant Subspace

Abstract

Formulas for the dimension vectors of all objects M in the category mathcal {S}(tilde {6}) of nilpotent operators with nilpotency degree bounded by 6, acting on finite dimensional vector spaces with invariant subspaces in a graded sense, are given (Theorem 2.3). For this purpose we realize a tubular algebra Λ, controlling the category mathcal {S}(tilde {6}), as an endomorphism algebra of a suitable tilting bundle over a weighted projective line of type (2,3,6) (Theorem 3.6). Using this description and a concept of mono-epi type, the interval multiplicity vector of an object in mathcal {S}(tilde {6}) is introduced and determined (Theorem 2.8). This is a much finer invariant than the usual dimension vector.