论文标题
PBW参数化和广义前预设代数
PBW parametrizations and generalized preprojective algebras
论文作者
论文摘要
geißleclerc-Schröer[发明。数学。 209（2017）]引入了与广义cartan矩阵及其对称器相关的广义前章节代数的概念。这类代数在nilpotent品种的最大尺寸不可还原成分[selecta Math。 （N.S.）24（2018）]。对于一般有限类型，我们通过在Weyl组的广义前前代数模块类别中通过部分扭转类别的部分顺序对这些组件进行分层。此外，我们从这些组件的通用模块中实现了Mirković-Vilonen多面体，并在Mirković-Vilonen多面体和一组最大尺寸不可舒服的成分之间鉴定为晶体。这概括了Baumann-Kamnitzer的结果[代表。理论16（2012）]和Baumann-Kamnitzer-Tingley [Publ。数学。研究高级科学。 120（2014）]。
Geiß-Leclerc-Schröer [Invent. Math. 209 (2017)] has introduced a notion of generalized preprojective algebra associated with a generalized Cartan matrix and its symmetrizer. This class of algebra realizes a crystal structure on the set of maximal dimensional irreducible components of the nilpotent variety [Selecta Math. (N.S.) 24 (2018)]. 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 [Represent. Theory 16 (2012)] and Baumann-Kamnitzer-Tingley [Publ. Math. Inst. Hautes Études Sci. 120 (2014)].
