PBW parametrizations and generalized preprojective algebras
PBW parametrizations and generalized preprojective algebras
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DOI：
10.1016/j.aim.2021.108144
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发表时间：
2020-11
影响因子：
1.7
通讯作者：
K. Murakami
中科院分区：
文献类型：
--
作者：
K. Murakami
Geiß-Leclerc-Schröer(2017)[24]引入了与广义Cartan矩阵及其对称子相关的广义预投影代数的概念。这些代数在幂零变体的最大维不可约分量集上实现晶体结构（Geiss et al. 2018,[26]）。对于一般有限型，我们通过Weyl群的广义预射影代数模范畴中扭转类的偏序给出了这些分量的分层。此外，我们从这些分量的一般模中实现了Mirković-Vilonen多面体，并给出了Mirković-Vilonen多面体集与最大维不可约分量集之间的晶体识别。这概括了Baumann-Kamnitzer(2012)[8]和Baumann-Kamnitzer- tingley(2014)[10]的结果。
Geiß-Leclerc-Schröer (2017) [24] has introduced a notion of generalized preprojective algebras associated with generalized Cartan matrices and their symmetrizers. These algebras realize crystal structures on the set of maximal dimensional irreducible components of the nilpotent varieties (Geiss et al. 2018, [26]). For general finite types, we give stratifications of these components via partial orders of torsion classes in module categories of generalized preprojective algebras in terms of Weyl groups. In addition, we realize Mirković-Vilonen polytopes from generic modules of these components, and give an identification as crystals between the set of Mirković-Vilonen polytopes and the set of maximal dimensional irreducible components. This generalizes results of Baumann-Kamnitzer (2012) [8] and Baumann-Kamnitzer-Tingley (2014) [10].