Felix Noeske

Condensation of homomorphism spaces

We present an ecient algorithm for the condensation of homomorphism spaces. This provides an improvement over the known tensor condensation method which is essentially due to a better choice of bases. We explain the theory behind this approach and describe the implementation in detail. Finally, we give timings to compare with previous methods.

Matching Simple Modules of Condensed Algebras

Let A be a finite dimensional algebra over a finite field F . Condensing an A-module V with two different idempotents e and e′ leads to the problem that to compare the composition series of V e and V e′, we need to match the composition factors of both modules. In other words, given a composition factor S of V e, we have to find a composition factor S′ of V e′ such that there exists a composition factor Ŝ of V with Ŝe ∼= S and Ŝe′ ∼= S′, or prove that no such S′ exists. In this note, we present a computationally tractable solution to this problem.

Restricting unipotent characters in special orthogonal groups

For all prime powers q we restrict the unipotent characters of the special orthogonal groups SO5(q) and SO7(q) to a maximal parabolic subgroup. We determine all irreducible constituents of these restrictions for SO5(q) and a large part of the irreducible constituents for SO7(q).

Matching simple modules of condensation algebras

We revise the matching algorithm of Noeske ( LMS J. Comput. Math. 11 (2008) 213–222) and introduce a new approach via composition series to expedite the calculations. Furthermore, we show how the matching algorithm may be applied in the more general and frequently occurring setting that we are only given subalgebras of the condensed algebras which each contain the separable algebra of one of their Wedderburn–Malcev decompositions.

The imprimitive faithful complex characters of the Schur covers of the symmetric and alternating groups

Abstract Using combinatorics and character theory, we determine the imprimitive faithful complex characters, i.e., the irreducible faithful complex characters which are induced from proper subgroups, of the Schur covers of the symmetric and alternating groups. Furthermore, for every imprimitive character we establish all its minimal block stabilizers. As a corollary, we also determine the monomial faithful characters of the Schur covers.