On some Ringel-Hall polynomials associated to tame indecomposable modules

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Let k be a finite field and Q an acyclic quiver of tame type (i.e. of type A˜m,D˜m,E˜6,E˜7,E˜8). Consider the path algebra kQ and the category of finite dimensional right modules mod-kQ. Using Schofield induction combined with some reduction tools, we determine all the Ringel-Hall polynomials associated to indecomposable modules of defect ranging from −2 to 2. In this way we obtain the full list of Ringel-Hall polynomials corresponding to indecomposables in the tame cases A˜m, D˜m and a partial list in the tame cases E˜6, E˜7, E˜8.