Trivial source character tables of SL(2,q)

Abstract

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL2(q) over a large enough field k of positive characteristic ℓ via character-theoretical methods in the cases in which q is odd, ℓ | (q ± 1) when ℓ is odd, and q ≡ ±3 (mod 8) when ℓ = 2.