Parabolic subgroups and induced characters
Meinolf Geck, Golz Pfeiffer · 2000
Abstract In Chapter 5, we determined the irreducible characters for each finite Coxeter group W. For the exceptional types, this was done using some explicit computations, which yield the complete character tables. For the classical types, we described explicit constructions which yield parametrizations of the irreducible characters in terms of partitions or pairs of partitions. Now we are interested in finding systematic ways (valid for all types) of describing the irreducible characters of Win terms of the induction of characters from parabolic subgroups. Of course, we cannot expect to obtain a nice theory when we just look at all parabolic subgroups and all constituents of all induced characters. However, it turns out that we do obtain interesting results when we impose restrictions either on the choice of the characters that are induced or on the irreducible constituents that we consider in a given induced character.