Representations of Finite Groups of Lie Type

François Digne; Jean Michel

doi:10.1017/CBO9781139172417

This book is based on a graduate course taught at the University of Paris. The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the Curtis–Alvis duality map and Mackey's theorem and the results that can be deduced from it. They also discuss Deligne–Lusztig induction. This will be the first elementary treatment of this material in book form and will be welcomed by beginning graduate students in algebra.

"...clearly written, well-organized, and has proofs wherever possible. There are also many examples illustrating the theory." Bhama Srinivasan, Mathematical Reviews

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Introduction
pp 1-4
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0 - Basic results on algebraic groups
pp 5-18
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1 - The Bruhat decomposition; parabolic subgroups
pp 19-27
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2 - Intersections of parabolic subgroups
pp 28-32
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3 - Rationality, Frobenius endomorphism
pp 33-44
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4 - Harish-Chandra induction and restriction
pp 45-50
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5 - The Mackey formula
pp 51-56
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6 - Harish-Chandra's theory
pp 57-60
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7 - Further results on Harish-Chandra induction
pp 61-62
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8 - The duality functor
pp 63-71
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9 - The Steinberg character
pp 72-75
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10 - l-adic cohomology
pp 76-80
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11 - Deligne-Lusztig induction; the Mackay formula
pp 81-89
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12 - The character formula and other results
pp 90-99
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13 - Geometric conjugacy and Lusztig series
pp 100-118
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14 - Regular elements; Gelfand-Graev representations
pp 119-142
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15 - Examples
pp 143-155
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Bibliography
pp 156-157
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Index
pp 158-159
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Representations of Finite Groups of Lie Type

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp 1-4

0 - Basic results on algebraic groups
pp 5-18

1 - The Bruhat decomposition; parabolic subgroups
pp 19-27

2 - Intersections of parabolic subgroups
pp 28-32

3 - Rationality, Frobenius endomorphism
pp 33-44

4 - Harish-Chandra induction and restriction
pp 45-50

5 - The Mackey formula
pp 51-56

6 - Harish-Chandra's theory
pp 57-60

7 - Further results on Harish-Chandra induction
pp 61-62

8 - The duality functor
pp 63-71

9 - The Steinberg character
pp 72-75

10 - l-adic cohomology
pp 76-80

11 - Deligne-Lusztig induction; the Mackay formula
pp 81-89

12 - The character formula and other results
pp 90-99

13 - Geometric conjugacy and Lusztig series
pp 100-118

14 - Regular elements; Gelfand-Graev representations
pp 119-142

15 - Examples
pp 143-155

Bibliography
pp 156-157

Index
pp 158-159

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