24 citations · 101 across the 31 of their papers we have counts for
34 papers
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…
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…
Unitary representations of real groups and localization theory for Hodge modules
Dougal Davis, Kari Vilonen
We prove a conjecture of Schmid and the second named author that the unitarity of a representation of a real reductive Lie group with real infinitesimal character can be read off f…
Hodge Filtrations on Tempered Hodge Modules
Dougal Davis, Kari Vilonen
We show that the Hodge filtration of a tempered Hodge module is generated by the lowest piece of its Hodge filtration. As a consequence, we prove the main conjecture of [SV] in the…
Mixed Hodge modules and real groups
Dougal Davis, Kari Vilonen
Let be a complex reductive group, an involution, and . In arXiv:1206.5547, W. Schmid and the second named author proposed a program to study unitary…
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…