4 papers
The character sheaves on the group compactification
Xuhua He
We give a definition of character sheaves on the group compactification which is equivalent to Lusztig's definition in \cite{L3}. We also prove some properties of the character she…
Closures of Steinberg fibers in twisted wonderful compactifications
Xuhua He, Jesper Funch Thomsen
By a case-free approach we give a precise description of the closure of a Steinberg fiber within a twisted wonderful compactification of a simple linear algebraic group. In the non…
Unipotent variety in the group compactification
Xuhua He
The unipotent variety of a reductive algebraic group plays an important role in the representation theory. In this paper, we will consider the closure $\bar{\Cal U}$ of the uni…
Total positivity in the De Concini-Procesi compactification
Xuhua He
We study the nonnegative part \bar{G_{>0}} of the De Concini-Procesi compactification of a reductive algebraic group G, as defined by Lusztig. Using positivity properties of the ca…