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Calculations in character Hopf algebras using SCHUR and Maple

Symmetric functions provide a tool for computations in invariant theory and especially for group characters. Recently, developments in Hopf algebra have pushed forward these technologies to cope with a wide class of subgroups of GL(n). To be able to provide examples computer algebra computations are inevitable due to the inherent combinatorial complexity of the problem. We describe how SCHUR (B.G. Wybourne et al.) was used to compute characters of non-semisimple groups and what its benefits and deficiencies are. Furthermore we discuss the Maple package SchurFkt? (R. Ablamowicz, B. Fauser) which was designed to provide a proof-of-concept approach for new algorithms. Problems with data structures, efficiency etc. will be addressed.

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