Conjugacy action, induced representations and the Steinberg square for simple groups of Lie type

By G. Heide, Jan Saxl, Pham Huu Tiep, A. Zalesski. 2012

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Let G be a finite simple group of Lie type, and let πG be the permutation representation of G associated with the action of G on itself by conjugation. We prove that every irreducible complex representation of G is a constituent of πG, unless G=PSUn(q) and n⩾3 is coprime to 2(q+1), where precisely one irreducible representation fails. We also prove that every irreducible representation of G is a constituent of the tensor square St ⊗ St of the Steinberg representation St of G, with the same exceptions as in the previous statement.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b3cd196bc548da35a0d93150fee8fe8ac74d1201