Abstract
R.B.Howlett and G.I.Lehrer obtained a detailed description of the endo-morphism algebra of an induced cuspidal representation of a reductive group over a finite field. They conjectured (and proved in many cases) that this algebra is always isomorphic to the group algebra of a certain finite group. This conjecture is equivalent to the statement that the induced representation contains an irreducible constituent with multi-plicty 1. G.Lusztig has shown that this is true for groups with connected centre. In this note, we characterize such an irreducible constituent with multiplicity I by its degree and deduce from this result, using regular embeddings and Clifford theory, that Howlett's and LehreFs conjecture holds in general.
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