Blocks of Lie Superalgebras of Type W(n)

Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [8]. This leads to a classification problem. For example, in [4], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ≥ 2, and by giving an explicit description of the indecomposable finite-dimensional representations of sl(1, n). When g is of type W (0, n), the irreducible finite-dimensional g-modules are classified in [1]; in this paper, we investigate finite-dimensional indecomposable modules. We show that the category of finite-dimensional representations of g is wild (i.e., as hard as classifying pairs of matrices; q.v. §2) when g is of type W (0, n) with n ≥ 3. More precisely, the category of finite-dimensional representations decomposes into blocks parametrised by (