5 papers
Cuspidal character sheaves on graded exceptional Lie algebras: stable gradings
Ting Xue
We determine cuspidal character sheaves explicitly for all (GIT) stably graded exceptional Lie algebras.
Cuspidal character sheaves on graded Lie algebras
Wille Liu, Cheng-Chiang Tsai, Kari Vilonen +1
We show in this paper that in the context of graded Lie algebras, all cuspidal character sheaves arise from a nearby-cycle construction followed by a Fourier--Sato transform in a v…
Cuspidal character sheaves on graded Lie algebras II
Wille Liu, Kari Vilonen, Ting Xue
In this paper we give a complete classification of cyclically graded semisimple Lie algebras that afford cuspidal character sheaves and determine the support of the cuspidal charac…
Nearby Cycle Sheaves for Stable Polar Representations
Mikhail Grinberg, Kari Vilonen, Ting Xue
Let G|V, G connected, reductive over C, be a stable polar representation in the sense of [DK], satisfying some mild additional hypotheses. Given a G-equivariant rank one local syst…
Invariant systems and character sheaves for graded Lie algebras
Kari Vilonen, Ting Xue
In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we constru…