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Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting. This book focuses on the smallest non-trivial example, namely the group SL2(Fq), which not only provide the simplicity required for a complete description of the theory, but also the richness needed for illustrating the most delicate aspects.

The development of Deligne-Lusztig theory was inspired by Drinfeld's example in 1974, and Representations of SL2(Fq) is based upon this example, and extends it to modular representation theory. To this end, the author makes use of fundamental results of l-adic cohomology. In order to efficiently use this machinery, a precise study of the geometric properties of the action of SL2(Fq) on the Drinfeld curve is conducted, with particular attention to the construction of quotients by various finite groups.

At the end of the text, a succinct overview (without proof) of Deligne-Lusztig theory is given, as well as links to examples demonstrated in the text. With the provision of both a gentle introduction and several recent materials (for instance, Rouquier's theorem on derived equivalences of geometric nature), this book will be of use to graduate and postgraduate students, as well as researchers and lecturers with an interest in Deligne-Lusztig theory.

- Series:
**Algebra and Applications 13** - Author:
**CĂ©dric BonnafĂ© (auth.)** - Year:
**2011** - Publisher:
**Springer-Verlag London** - Language:
**English** - ISBN:
**0857291564,9780857291561**

- File size:
**1 314 242** - Format:
**pdf**

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This book addresses Lie groups, Lie algebras, and representation theory. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader ...

Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. Michael Cowling presents a survey of various interactions between representation...

Design representation is necessary for all design activity. You will gain a guide to both theory and practical application in this discussion of representation as it occurs during the process of design. Goldschmidt and Porter give you perspectives on repr...

In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zpwhich are the inverse limit of the finite rings Z/pn. This gives rise to a...

This is the second edition of the popular textbook on representation theory of finite groups. The authors have revised the text greatly and included new chapters on Characters of GL(2,q) and Permutations and Characters. The theory is developed in terms of...

Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups al...

In the field of genetic and evolutionary algorithms (GEAs), much theory and empirical study has been heaped upon operators and test problems, but problem representation has often been taken as given. This monograph breaks with this tradition and studies a...

The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois represen...

The major achievements of mathematical analysis from Newton and Euler to modern applications of mathematics in physical sciences, engineering and other areas are presented in this volume. Its three parts cover the methods of analysis: representation metho...

This volume addresses the interplay between representation theory and automorphic forms. The invited papers, written by leading mathematicians, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their as...

Volume 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and mathematics as an art. Specific contri...

Volume 4 of a monumental 4-volume set covers such topics as mathematical machines, mathematics in warfare, a mathematical theory of art, mathematics of the good, mathematics in literature, mathematics and music, and amusements, puzzles, and fancies. Indiv...

Volume 1 of a monumental 4-vol. set includes a general survey of mathematics; historical and biographical information on prominent mathematicians throughout history; material on arithmetic, numbers and the art of counting, and the mathematics of space and...

The Worlds of Medieval Europe updates and revises traditional textbook representations of the Middle Ages by balancing the conventional focus on political affairs, especially those of northern Europe, with equally detailed attention to medieval society as...

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First published in 1979, The World of Goods rapidly established itself as a classic. In this pioneering work, a leading anthropologist and an economist join forces to suggest what market researchers have long suspected and anthropologists have observed fi...

A closer look into the making and workings of the Jinn and Devils. It answers many of our questions as to what they eat, whether or not they marry and where they reside. It points out the goals, means and plots of Satan against the Human. It includes ...

This course examines the development of the British Empire from the death of Queen Victoria in 1901, via its greatest territorial extent in 1919 to its eventual decline and end in the years after World War II, and its final transformation into the commonw...

This course examines the growth and development of the largest empire in world history, the British Empire, beginning with the late 15th-century Tudor dynasty and ending with the death of Queen Victoria in 1901....