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Showing 1 to 11 of 11 for “"Modular Representation Theory"”.
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On hochschild cohomology and modular representation theory
… is to study local and global invariants in representation theory of finite groups using the (restricted) Lie algebra structure of the first degree of Hochschild cohomology of a block algebra B as a main tool. This lead to two directions: In the first part we investigate the global approach. …
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Über die Elementarteiler der Inzidenzmatrix des Ree-Unitals
… of this group, we apply some methods of module theory and of modular representation theory. A complete determination of the structure fails in the general case. However, we can reduce the number of possibilities for the 2-component to three. In certain cases we succeed in completely determining …
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Formulae for symmetric powers and tensor products of modular representations of elementary abelian p-groups
In the landscape of modular representation theory, the study of decomposition formulas for symmetric powers and tensor products in the context of elementary abelian p-groups remains underdeveloped in the existing literature. This research addresses this gap by systematically developing explicit …
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The representation theory of diagram algebras
In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it …
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Charaktertafeln parabolischer Untergruppen der Steinbergschen Trialitätsgruppen und Anwendungen auf deren Darstellungstheorie
… groups are determined. Then, by Clifford theory, the generic character table of a maximal parabolic subgroup and a large part of the generic character table of another maximal parabolic subgroup are computed. In 1990, M. Geck has determined the decomposition numbers of Steinberg's triality …
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Untersuchungen zu Tensorprodukten von Moduln symmetrischer Gruppen
… finite group occur in many areas of ordinary and modular representation theory. In general only little is known about the structure of these modules. This thesis is about various aspects of tensor products of modules of symmetric groups S_n over a field of prime characteristic p. The main focus …
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Endomorphismenringe von Permutationsmoduln auf den Nebenklassen einer p-Sylowgruppe
… first, fundamental elements of the ordinary and modular representation theory of such endomorphism rings are analyzed and compared with the corresponding structures of the underlying group. This enables us to derive criterions for projective simplicity for ordinary characters of the …
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Modular Temperley-Lieb Theory
This dissertation considers the representation theory of Temperley-Lieb algebras, TLₙ , along with some related cellular algebras, over positive and mixed characteristic fields. The Temperley-Lieb algebras are planar diagrammatic algebras. They are generated by “(n, n)-diagrams”: planar pair …
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Group rings over the p-adic integers
… over the p-Adic Integers" is concerned with the representation theory of finite groups over the ring of p-adic integers (or, usually, an algebraic extension thereof). It deals with blocks of special linear groups of degree two, blocks of dihedral defect and blocks of symmetric groups. In each …
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Combinatorial Methods in the Representation Theory of the Symmetric Group
The study of the representation theory of the symmetric group can be carried out from a combinatorial point of view, avoiding the machinery of the representation theory of algebraic groups. This approach has the benefit of providing more insight into the subject as the study remains in the setting …
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Semisimple filtrations of tilting modules for algebraic groups
… weight, form an important class of self-dual representations over $k$. In this thesis we investigate semisimple filtrations of minimal length (Loewy series) of tilting modules. We first demonstrate a criterion for determining when tilting modules for arbitrary quasi-hereditary algebras are …