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Deformations of Inhomogeneous Simple Singularities and Quiver Representations
Algebras and Representation Theory ( IF 0.6 ) Pub Date : 2020-03-19 , DOI: 10.1007/s10468-019-09927-y
Antoine Caradot

This article is a summary of the author’s unpublished Ph.D thesis (Caradot 2017). Its purpose is to generalise a construction by H. Cassens and P. Slodowy of the semiuniversal deformations of the simple singularities of type Ar, Dr, E6, E7 and E8 to the inhomogeneous simple singularities of type Br, Cr, F4 and G2. To a homogeneous simple singularity, one can associate the representation space of a particular quiver. This space is endowed with an action of the symmetry group of the Dynkin diagram associated to the simple singularity. From this we will construct and compute explicitly the semiuniversal deformations of the inhomogeneous simple singularities. By quotienting such maps, we obtain deformations of other simple singularities. In some cases, the discriminants of these last deformations will be computed.



中文翻译:

非均匀简单奇异点和颤动表示的变形

本文是作者未发表的博士学位论文摘要(Caradot 2017)。它的目的是将H. Cassens和P.Slovodoy的构造推广为A rD rE 6E 7E 8型简单奇点的半普遍变形为B rC型不均匀单奇点的构造rF 4G 2。对于同质的简单奇点,可以将特定颤抖的表示空间关联起来。该空间具有与简单奇异性相关的Dynkin图对称组的作用。由此,我们将显式构造和计算不均匀简单奇异点的半普遍变形。通过对这些图进行商定,我们可以获得其他简单奇点的变形。在某些情况下,将计算这些最后变形的判别式。

更新日期:2020-03-19
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