On the labelling of characters of Weyl groups of type $$F_4$$

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, vol. 65, pp. 853–866

Abstract

Abstract In the literature on finite groups of Lie type, there exist two different conventions about the labelling of the irreducible characters of Weyl groups of type $$F_4$$ F 4 . We point out some issues concerning these two conventions and their effect on tables about unipotent characters or the Springer correspondence. Using experiments related to these issues with the computer algebra system , we spotted an error in Spaltenstein’s tables for the generalised Springer correspondence in type $$E_7$$ E 7 .

Authors 2

1. Meinolf Geck

   University of Stuttgart

   Affiliation as printed

   FB Mathematik, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

2. Jonas Hetz corresponding Aachen Lehrstuhl für Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl für Algebra und Zahlentheorie, RWTH Aachen, Pontdriesch 14/16, 52062, Aachen, Germany