Errata and notes on the paper "A generalization of Springer theory using nearby cycles"

A generalization of Springer theory using nearby cycles

Let g be a complex semisimple Lie algebra, and f : g --> g/G the adjoint quotient map. Springer theory of Weyl group representations can be seen as the study of the singularities of f. We give a generalization of Springer theory to visible, polar representations. It is a class of rational representations of complex reductive groups, for which the invariant theory works by analogy with the adjoint representations. Let G|V be such a representation, f : V --> V/G the quotient map, and P the sheaf of nearby cycles of f. We show that the Fourier transform of P is an intersection homology sheaf on V…

对称对的邻近循环层

Nearby Cycle Sheaves for Symmetric Pairs

该研究在对称空间框架下提出邻近循环层构造，可作为经典Springer理论中Grothendieck-Springer解消的替代方案。