113 research outputs found
Rationality properties of unipotent representations
We describe those unipotent representations of a finite group of Lie type
which are defined over the rational numbers.Comment: 14 page
Elliptic Weyl group elements and unipotent isometries with p=2
Let G be a classical group over an algebraically closed field of
characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In
a previous paper the first named author associated to C a unipotent conjugacy
class \Phi(C) in G. In this paper we show that \Phi(C) can be characterized in
terms of the closure relations between unipotent classes. Previously the
analogous result was known in odd characteristic and for exceptional groups in
any characteristic.Comment: 7 page
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.Comment: 21 page
Endoscopy for Hecke categories, character sheaves and representations
For a split reductive group over a finite field, we show that the neutral
block of its mixed Hecke category with a fixed monodromy under the torus action
is monoidally equivalent to the mixed Hecke category of the corresponding
endoscopic group with trivial monodromy. We also extend this equivalence to
all blocks. We give two applications. One is a relationship between character
sheaves on with a fixed semisimple parameter and unipotent character
sheaves on the endoscopic group , after passing to asymptotic versions. The
other is a similar relationship between representations of
with a fixed semisimple parameter and unipotent representations of
.Comment: 57 pages. A new section on application to representations added. A
few small gaps fixed. To appear in Forum of Mathematics P
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