15 citations · 32 across the 12 of their papers we have counts for
16 papers
Representations with the same degree
Frank Lübeck
In this short note we show that every connected reductive simply-connected algebraic group of rank over the complex numbers has infinitely many pairs of irreducible representa…
The irreducible Brauer characters of the automorphism group of the Chevalley group F_4(2)
Gerhard Hiss, Frank Lübeck
Using computational methods, we determine the irreducible Brauer characters of the automorphism group of the Chevalley group F_4(2), up to one parameter and one consistency issue.
Generalized Green functions and unipotent classes for finite reductive groups, IV
Frank Lübeck, Toshiaki Shoji
In this paper, we formulate the notion of split elements of a unipotent class in a connected reductive group . Generalized Green functions of can be computed by using Luszti…
Green Functions in Small Characteristic
Frank Lübeck
The values of the ordinary Green functions are known for almost all groups of Lie type, a long term achievement by various authors. In this note we solve the last open cases, which…
Greatest common divisors of values of integer polynomials and an application to maximal tori
Frank Lübeck
We describe how to compute for two polynomials with integer coefficients the greatest common divisors of and for all integers $z \in \m…
Standard Generators of Finite Fields and their Cyclic Subgroups
Frank Lübeck
We define standardized constructions of finite fields, and standardized generators of (multiplicative) cyclic subgroups in these fields. The motivation is to provide a substitute f…
The inductive blockwise Alperin weight condition for the Chevalley groups
Jianbei An, Gerhard Hiss, Frank Lübeck
We verify the inductive blockwise Alperin weight condition in odd characteristic for the finite exceptional Chevalley groups for not divisible by .
Orbits of in Dimension 8
Frank Lübeck
Groups of structure have an irreducible representation of degree which can be realized over and any prime field . This representation ex…
Remarks on computing Green functions
Frank Lübeck
We describe the computation of generalized Green functions and 2-parameter Green functions for finite reductive groups.
Zero-one generation laws for finite simple groups
Robert M. Guralnick, Martin W. Liebeck, Frank Lübeck +1
Let be a simple algebraic group over the algebraic closure of ( prime), and let denote a corresponding finite group of Lie type over , where is a p…
Turning Weight Multiplicities into Brauer Characters
Frank Lübeck
We describe two methods for computing -modular Brauer character tables for groups of Lie type in defining characteristic , assuming that the ordinary character table…
Computation of Kazhdan-Lusztig polynomials and some applications to finite groups
Frank Lübeck
We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig polynomials. As an application we compute Kazhdan-Lusztig polynomials which are needed to evaluate a character…
Characters and Brauer trees of the covering group of
Frank Lübeck
Let be the finite simple Chevalley group of type . It has a Schur multiplier of type . We determine the ordinary character tables of the central ext…
Rigidity for F_4(p)
Frank Lübeck, Robert Guralnick, Jun Yu
We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and s…
Primitive prime divisors and the -th cyclotomic polynomial
S. P. Glasby, Frank Lübeck, Alice C. Niemeyer +1
Primitive prime divisors play an important role in group theory and number theory. We study a certain number theoretic quantity, called , which is closely related to the…
On defining characteristic representations of finite reductive groups
Olivier Brunat, Frank Lübeck
We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.