Preface

Summary

“I confess I like to take account of possibilities. Don't you know mathematics are my hobby? Did you ever study algebra? I always have an eye on the unknown quantity”.

Henry James, The Story of a Year

Ich predige die Mathematik … … Die Beschäftigung mit der Mathematik, sage ich, ist das beste Mittel gegen die Kupiditäat. Staatsanwalt Paravant, der stark angefochten war, hat sich drauf geworfen, er hat es jetzt mit der Quadratur des Kreises und spürt große Erleichterung.

Thomas Mann, Der Zauberberg

– Ah! c'etait impossible, les cours duraient parfois fort tard.

– Même après 2 heures du matin? demandait le baron.

– Des fois.

– Mais l'algèbre s'apprend aussi facilement dans un livre.

– Même plus facilement, car je ne comprends pas grand' chose aux cours.

– Alors? D'ailleurs l'algèbre ne peut te servir à rien.

– J'aime bien cela. Ca dissipe ma neurasthénie.

Marcel Proust, Sodome et Gomorrhe

Whatever its therapeutic value may be, group theory offers plenty of diversions and challenges. In particular, the study of finite groups of Lie type and their representations (ordinary or modular) leads to deep questions, many of which are still unsolved.

A more accurate but cumbersome title for this book would be: “A guide to the modular representation theory of finite groups of Lie type in the defining characteristic p”. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne–Lusztig characters.