Frank Himstedt
Dade's Invariant Conjecture for the Ree groups 2F4(q^2) in Defining Characteristic.
Mon, 03/08/2010 - 16:01 — SomNambulAuthors: Frank Himstedt, Shih-chang Huang
Subjects: Representation Theory
AbstractWe verify Dade's invariant conjecture for the simple Ree groups 2F4(2^{2n+1})
for all n > 0 in the defining characteristic, i.e., in characteristic 2. This
completes the proof of Dade's conjecture for the simple Ree groups
2F4(2^{2n+1}).On the restriction of cross characteristic representations of ^2F_4(q) to proper subgroups.
Tue, 10/27/2009 - 16:01 — SomNambulAuthors: Frank Himstedt, Hung Ngoc Nguyen, Pham Huu Tiep
Subjects: Representation Theory
AbstractWe prove that the restriction of any nontrivial representation of the Ree
groups $^2F_{4}(q), q=2^{2n+1}\geq8$ in odd characteristic to any proper
subgroup is reducible. We also determine all triples $(K, V, H)$ such that $K
\in \{^2F_4(2), ^2F_4(2)'\}$, $H$ is a proper subgroup of $K$, and $V$ is a
representation of $K$ in odd characteristic restricting absolutely irreducibly
to $H$.On the Decomposition Numbers of the Ree Groups 2F4(q^2) in Non-Defining Characteristic.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Frank Himstedt
Subjects: Representation Theory
AbstractWe compute the l-modular decomposition matrices of the simple Ree groups
2F4(q^2), where q^2=2^{2n+1} and n is a positive integer, for all primes l > 3
up to some entries in the unipotent characters. Using these matrices we
determine the smallest degree of a non-trivial irreducible l-modular
representation of 2F4(q^2) for all primes l > 3. We also obtain results on the
3-modular decomposition matrices of 2F4(q^2).On the Decomposition Numbers of the Ree Groups 2F4(q^2) in Non-Defining Characteristic.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Frank Himstedt
Subjects: Representation Theory
AbstractWe compute the l-modular decomposition matrices of the simple Ree groups
2F4(q^2), where q^2=2^{2n+1} and n is a positive integer, for all primes l > 3
up to some entries in the unipotent characters. Using these matrices we
determine the smallest degree of a non-trivial irreducible l-modular
representation of 2F4(q^2) for all primes l > 3. We also obtain results on the
3-modular decomposition matrices of 2F4(q^2).On equivariant bijections relative to the defining characteristic.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Olivier Brunat, Frank Himstedt
Subjects: Representation Theory
AbstractThis paper is a contribution to the general program introduced by Isaacs,
Malle and Navarro to prove the McKay conjecture in the representation theory of
finite groups. We develop new methods for dealing with simple groups of Lie
type in the defining characteristic case. Using a general argument based on the
representation theory of connected reductive groups with disconnected center,
we show that the inductive McKay condition holds if the Schur multiplier of the
simple group has order 2.
User login
