Deligne-Lusztig Seminar (Lent 2022)

This study group is loosely organized around further developments in Deligne-Lusztig theory. The goal is to gain some broad exposure to the circle of ideas in the subject without focusing too heavily on any particular proof.

We meet on Thursdays at 2:30 pm in MR11. Anyone is welcome to participate!

References for talks

General references

• Representations of reductive groups over finite fields (Deligne and Lusztig)
• Finite groups of Lie type (Carter)
• Representations of finite groups of Lie type (Digne and Michel)
• Algebraic and geometric methods in representation theory (Lusztig)

Examples

• The characters of the finite general linear groups (Green)
• The characters of the finite symplectic group Sp(4,q) (Srinivasan)
• The characters of the finite unitary groups (Lusztig and Srinivasan)

Affineness of Deligne-Lusztig varieties

• Deligne-Lusztig varieties and period domains over finite fields (Orlik and Rapoport)
• Affineness of Deligne-Lusztig varieties for minimal length elements (Bonnafé and Rouquier)
• On the affineness of Deligne-Lusztig varieties (He)

Hecke algebras and intertwining operators

• Eisenstein series over finite fields (Harish-Chandra)
• Induced cuspidal representations and generalised Hecke rings (Howlett and Lehrer)
• A note on Harish-Chandra induction (Geck)
• Nonexistence of twisted Hecke algebras (Gyoja)

Alvis-Curtis duality

• The duality operation in the character ring of a finite Chevalley group (Alvis)
• Truncation and duality in the character ring of a finite group of Lie type (Curtis)
• Duality for representations of a finite reductive group over a finite field I and II (Deligne and Lusztig)

Lusztig series and unipotent representations

• Characters of reductive groups over a finite field (Lusztig)
• Representations of finite Chevalley groups (Lusztig)

Character sheaves

• Introduction to character sheaves (Lusztig)
• Faisceaux caractères (Laumon)
• A first guide to the character theory of finite groups of Lie type (Geck)