Abstract: I shall first explain a "Fourier transform" in [1] relating endomorphism algebras of Gelfand--Graev representations to Grothendieck rings of modular representations, and then, following [2], use this Fourier transform to partially refine a result of Bonnafe--Kessar on the saturatedness of Curtis homomorphisms.

References:
[1] T.-J. Li and J. Shotton, On endomorphism algebras of Gelfand–Graev representations II, Bull. LMS (2023)
[2] T.-J. Li, On integral images of Curtis homomorphisms for $GL_n$ and $U_n$, preprint (arXiv:2401.04989v1)