Formulae for two-variable Green functions

François Digne (1) , Jean Michel (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

Based on results of Digne-Michel-Lehrer (2003) we give two formulae for two-variable Green functions attached to Lusztig induction in a finite reductive group. We present applications to explicit computation of these Green functions, to conjectures of Malle and Rotilio, and to scalar products between Lusztig inductions of Gelfand-Graev characters.

Mots clés: Two variable Green functions; Lusztig induction

Domaines: Mathématiques [math]

François Digne, Jean Michel. Formulae for two-variable Green functions. Journal of Algebra, 2022, 610, pp.270-280. ⟨10.1016/j.jalgebra.2022.06.024⟩. ⟨hal-03880360⟩