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arXiv · 2001.11310

Complexity and Support Varieties for Type P Lie Superalgebras

Brian D. Boe·Jonathan R. Kujawa
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Abstract

We compute the complexity, z-complexity, and support varieties of the (thick) Kac modules for the Lie superalgebras of type P. We also show the complexity and the z-complexity have geometric interpretations in terms of support and associated varieties; these results are in agreement with formulas previously discovered for other classes of Lie superalgebras. Our main technical tool is a recursive algorithm for constructing projective resolutions for the Kac modules. The indecomposable projective summands which appear in a given degree of the resolution are explicitly described using the combinatorics of weight diagrams. Surprisingly, the number of indecomposable summands in each degree can be computed exactly: we give an explicit formula for the corresponding generating function.

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Brian D. Boe, Jonathan R. Kujawa. 2020-01-30. Complexity and Support Varieties for Type P Lie Superalgebras. https://arxiv.org/abs/2001.11310

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