Generic Character Tables in GAP

• Applicant: Dr. Frank Lübeck
• Subject Area: Mathematics
• Term: from 2010 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 171203858

A character table encodes concisely and efficiently a lot of information about a particular finite group. In this project we consider generic character tables which describe and parameterize the character tables of certain infinite series of groups. The series of groups we consider are finite groups of Lie type. The classification of finite simple groups shows that most simple groups are closely related to finite groups of Lie type. The main aim of the proposed project is to develop a new software package, called GenCharLib, containing generic character tables as well as programs to compute with them. This will be implemented in the computer algebra system GAP. GenCharLib will serve the needs of specialists in the area by facilitating further extensions and applications. It will also make generic character tables more accessible to mathematicians who are not specialists in this field. Finally, it will enhance existing GAPfunctions automatically, by providing missing methods for some computations. The package GenCharLib will build upon experience with a previous package that was based on the computer algebra system Maple. This is a subproject of the CHEVIE project which provides computational access to the representation theory of finite groups of Lie type and related structures. The proposed project was already mentioned under point (PB5) of the proposal for the Priority Programme 1489.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory