arXiv subjects

George Lusztig

Publications and source records attributed to George Lusztig.

22 records · Page 2Linked to original sources

arXiv2011

A generalization of Steinberg's cross-section

Let G be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element w of minimal length r a subvariety V of G isomorphic to an affine space of dimension r which meets the regular unipotent class Y in exactly one point. In this paper this is generalized to the case where w is replaced by any elliptic element in the Weyl group of minimal length d in its conjugacy class, V is replaced by a subvariety V' of G isomorphic to an affine space of dimension d and Y is replaced by a unipotent class Y' of codimension d in such a way that the intersection of V' and Y' is finite.

math.RT↗

arXiv2007

Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups

In this paper we show how a theorem of Jantzen relating the character of a finite dimensional irreducible representation of a disconnected semisimple algebraic group on elements outside the connected component of identity to character of an irreducible representation of another connected semisimple algebraic group can be deduced from properties of the canonical bases.

math.RT↗

arXiv2005

Singular supports for character sheaves on a group compactification

Let $G$ be a semisimple adjoint group over $\bold C$ and $\bar{G}$ be the De Concini-Procesi completion of $G$. In this paper, we define a Lagrangian subvariety $Λ$ of the cotangent bundle of $\bar{G}$ such that the singular support of any character sheaf on $\bar{G}$ is contained in $Λ$.

math.RT↗

arXiv2001

Rationality properties of unipotent representations

We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.

math.RT↗