Abstract
Each exceptional object M in the category S(6˜) of nilpotent operators with nilpotency degree bounded by 6, acting on finite dimensional vector spaces with invariant subspaces in a graded sense, can be presented by matrices with 0-1 entries (Theorem 1.2). Moreover it, and even every member of all but one of the exceptional tubes, has the “interval tree”-property in the sense that the graph associated to the matrix of the structure map with respect to the interval decompositions of M restricted to the two copies of the cover of the algebra k[x]/(x6), is a tree (Theorem 1.7 and Corollary 1.8).
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