Ordinary and modular representations of Chevalley groups (Lecture notes in mathematics ; 528)

Science & Math

Humphreys, James E.

Mathematics

Springer, Verlag

James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

Linear Algebraic Groups (Graduate Texts in Mathematics, 21)

Springer

In this graduate textbook Professor Humphreys presents a concrete and up-to-date introduction to the theory of Coxeter groups. He assumes that the reader has a good knowledge of algebra, but otherwise the book is self contained. The first part is devoted to establishing concrete examples; the author begins by developing the most important facts about finite reflection groups and related geometry, and showing that such groups have a Coxeter representation. In the next chapter these groups are classified by Coxeter diagrams, and actual realizations of these groups are discussed. Chapter 3 discusses the polynomial invariants of finite reflection groups, and the first part ends with a description of the affine Weyl groups and the way they arise in Lie theory. The second part (which is logically independent of, but motivated by, the first) starts by developing the properties of the Coxeter groups. Chapter 6 shows how earlier examples and others fit into the general classification of Coxeter diagrams. Chapter 7 is based on the very important work of Kazhdan and Lusztig and the last chapter presents a number of miscellaneous topics of a combinatorial nature.

Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics, Series Number 29)

Cambridge University Press

In this graduate textbook Professor Humphreys presents a concrete and up-to-date introduction to the theory of Coxeter groups. He assumes that the reader has a good knowledge of algebra, but otherwise the book is self contained. The first part is devoted to establishing concrete examples; the author begins by developing the most important facts about finite reflection groups and related geometry, and showing that such groups have a Coxeter representation. In the next chapter these groups are classified by Coxeter diagrams, and actual realizations of these groups are discussed. Chapter 3 discusses the polynomial invariants of finite reflection groups, and the first part ends with a description of the affine Weyl groups and the way they arise in Lie theory. The second part (which is logically independent of, but motivated by, the first) starts by developing the properties of the Coxeter groups. Chapter 6 shows how earlier examples and others fit into the general classification of Coxeter diagrams. Chapter 7 is based on the very important work of Kazhdan and Lusztig and the last chapter presents a number of miscellaneous topics of a combinatorial nature.

Finite groups of Lie type encompass most of the finite simple groups. Their representations and characters have been studied intensively for half a century, though some key problems remain unsolved. This is the first comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne-Lusztig characters. One goal has been to make the subject more accessible to those working in neighboring parts of group theory, number theory, and topology.

Modular Representations of Finite Groups of Lie Type (London Mathematical Society Lecture Note Series, Series Number 326)

After the fundamental work of Borel and Chevalley in the 1950s and 1960s on the structure and classification of semisimple algebraic groups over an arbitrary algebraically closed field, further results were obtained on conjugacy classes and centralizers. Conjugacy Classes in Semisimple Algebraic Groups draws together results achieved by Lusztig, Richardson, Spaltenstein, Springer, Steinberg, and others. This book provides a unified exposition of work done over the past thirty years.

Conjugacy Classes in Semisimple Algebraic Groups (Mathematical Surveys & Monographs)

Amer Mathematical Society

This is the first textbook treatment of work leading to the landmark 1979 Kazhdan-Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra $\mathfrak{g}$ over $\mathbb {C}$. The setting is the module category $\mathscr {O}$ introduced by Bernstein-Gelfand-Gelfand, which includes all highest weight modules for $\mathfrak{g}$ such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of $\mathfrak{g}$. Basic techniques in category $\mathscr {O}$ such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan-Lusztig Conjecture (due to Beilinson-Bernstein and Brylinski-Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: $D$-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category $\mathscr {O}$, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson-Ginzburg-Soergel.

Representations of Semisimple Lie Algebras in the BGG Category O (Graduate Studies in Mathematics)

James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.

Linear Algebraic Groups (Graduate Texts in Mathematics)

This is an introductory text to lie algebras and representation theory. It covers areas such as semi-simple lie algebras, Chevalley algebras and groups, and isomorphism and conjugacy theorems.

Introduction to Lie algebras and representation theory (Graduate texts in mathematics)

Springer-Verlag Berlin and Hei

This text on linear algebraic groups includes areas such as: algebraic geometry; affine algebraic groups; Lie algebras; homogeneous spaces; characteristic 0 theory; and semisimple and unipoten elements.

Linear Algebraic Groups

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Books by Humphreys, James E.

See the best price to sell, buy, or rent books by Humphreys, James E.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Ordinary and modular representations of Chevalley groups (Lecture notes in mathematics ; 528)

Linear Algebraic Groups (Graduate Texts in Mathematics, 21)

Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics, Series Number 29)

Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics, Series Number 29)

Modular Representations of Finite Groups of Lie Type (London Mathematical Society Lecture Note Series, Series Number 326)

Conjugacy Classes in Semisimple Algebraic Groups (Mathematical Surveys & Monographs)

Representations of Semisimple Lie Algebras in the BGG Category O (Graduate Studies in Mathematics)

Linear Algebraic Groups (Graduate Texts in Mathematics)

Introduction to Lie algebras and representation theory (Graduate texts in mathematics)

Linear Algebraic Groups