Promotionen in der Computeralgebra

Abstract

Lukas Maas: Modular Spin Characters of Symmetric Groups ¨ ¨ Betreuer: Wolfgang Lempken (Essen), Jurgen Muller (Aachen/Essen) Zweitgutachter: Klaus Lux (University of Arizona, USA) Dezember 2011 http://www.iem.uni-due.de/~maas Zusammenfassung: The thesis is concerned with concrete computations of modular spin characters of symmetric and alternating groups. More precisely, we calculate all p-modular spin characters of the symmetric group Sn and the alternating group An for n {14, . . . , 18} and p {3, 5, 7}. Spin characters correspond to irreducible faithful representations of double cover~n and A ~n of Sn and An , respectively, and our reing groups S ~n and sults imply the p-modular decomposition numbers of S ~ An for the specified values of n and p. Indeed, still a key problem in the representation theory of (spin) symmetric groups is to find a general description of p-modular decomposition numbers. Our computational methods combine various techniques of algorithmic representation theory, namely the MOC system, the MeatAxe, and condensation, with procedures designed specifically for (spin) symmetric groups, for example, the construction of p-modular character tables of certain Young ~n and the explicit determination of their consubgroups of S jugacy class fusions. We used GAP for most of our computations, and the resulting data are stored as GAP-usable character tables. These are available from the author.