Multiplicity free induction for the pairs $({\mathrm{GL}}_2\times {\mathrm{GL}}_2,\mathrm{diag}({\mathrm{GL}}_2))$ and $({\mathrm{SL}}_3,{\mathrm{GL}}_2)$ over finite fields

Elias Depuydt, Maarten van Pruijssen

We classify the irredible representations of ${\mathrm{GL}}_2(q)$ for which the induction to the product group ${\mathrm{GL}}_2(q)\times {\mathrm{GL}}_2(q)$, under the diagonal embe…