论文标题
P型的复杂性和支持品种超级级别
Complexity and Support Varieties for Type P Lie Superalgebras
论文作者
论文摘要
我们计算了（厚）KAC模块的复杂性，Z复合度和支持P型的（厚）KAC模块的多种。这些结果与以前针对其他谎言超级级别类别的公式一致。 我们的主要技术工具是用于为KAC模块构建投影分辨率的递归算法。使用权重图的组合图明确地描述了以给定程度分辨率的不可分解的投影求和。令人惊讶的是，可以精确地计算每个程度中的不可分解的汇总数量：我们为相应的生成函数提供一个明确的公式。
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.
