Formulae for two-variable Green functions
Fran\c{c}ois Digne (LAMFA), Jean Michel (IMJ-PRG (UMR\_7586))
TL;DR
This paper presents explicit formulas for two-variable Green functions in finite reductive groups, enabling better computation and understanding of their properties, with applications to conjectures and scalar products involving Lusztig induction.
Contribution
It provides new explicit formulas for two-variable Green functions based on prior theoretical results, facilitating their computation and analysis.
Findings
Derived explicit formulas for two-variable Green functions
Applied formulas to compute scalar products of Lusztig inductions
Addressed conjectures of Malle and Rotilio
Abstract
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.
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