Abstract
The complexity of a module is the rate of growth of the minimal projective resolution of the module while the z-complexity is the rate of growth of the number of indecomposable summands at each step in the resolution. Let g=osp(k|2) (k>2) be the type II orthosymplectic Lie superalgebra of types B or D. In this paper, we compute the complexity and the z-complexity of the simple finite-dimensional g-supermodules. We then give these complexities certain geometric interpretations using support and associated varieties.
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