Complexity and Support Varieties for Type P Lie Superalgebras
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.
Cite
@article{arxiv.2001.11310,
title = {Complexity and Support Varieties for Type P Lie Superalgebras},
author = {Brian D. Boe and Jonathan R. Kujawa},
journal= {arXiv preprint arXiv:2001.11310},
year = {2020}
}
Comments
26 pages, 22 figures. A companion iOS app, Homologica, is available on the Apple App Store. Version 2: Minor corrections and changes suggested by the referee. To appear in Mathematical Research Letters