{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:61837"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:61837","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Unipotente Charaktere und Zerlegungszahlen der endlichen Chevalleygruppen vom Typ F 4","abstract":"This thesis contributes to the representation theory of finite Chevalleygroups. First we describe algorithms for explicit computation in connected reductive algebraic groups. These algorithms are well adapted to the computation in some finite subgroups, i.e., the finite groups of Lie type and their parabolic subgroups. Thus we can compute Bruhat decompositions, centralizers, conjugacy classes, fusions and intersection numbers of conjugacy classes with double cosets. The most crucial point is, that all these computations can be done for all finite fields simultaneously.Second we use these algorithms to determine the unipotent characters of the finite Chevalley groups of type F_4 as explicit class functions. This is done using the classification of these characters given by Deligne and Lusztig. We get further information by explicit Harish-Chandra induction, the construction of modified Gelfand-Graev characters. We compute some missing character values using Ree's character formula.Finally we compute large parts of the decomposition matrices of the unipotent blocks of these groups by constructing appropriate projective characters and using Brauer reciprocity.","abstract_html":"This thesis contributes to the representation theory of finite Chevalleygroups. First we describe algorithms for explicit computation in connected reductive algebraic groups. These algorithms are well adapted to the computation in some finite subgroups, i.e., the finite groups of Lie type and their parabolic subgroups. Thus we can compute Bruhat decompositions, centralizers, conjugacy classes, fusions and intersection numbers of conjugacy classes with double cosets. The most crucial point is, that all these computations can be done for all finite fields simultaneously.Second we use these algorithms to determine the unipotent characters of the finite Chevalley groups of type F_4 as explicit class functions. This is done using the classification of these characters given by Deligne and Lusztig. We get further information by explicit Harish-Chandra induction, the construction of modified Gelfand-Graev characters. 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First we describe algorithms for explicit computation in connected reductive algebraic groups. These algorithms are well adapted to the computation in some finite subgroups, i.e., the finite groups of Lie type and their parabolic subgroups. Thus we can compute Bruhat decompositions, centralizers, conjugacy classes, fusions and intersection numbers of conjugacy classes with double cosets. The most crucial point is, that all these computations can be done for all finite fields simultaneously.Second we use these algorithms to determine the unipotent characters of the finite Chevalley groups of type F_4 as explicit class functions. This is done using the classification of these characters given by Deligne and Lusztig. We get further information by explicit Harish-Chandra induction, the construction of modified Gelfand-Graev characters. 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