Character Theory and the McKay Conjecture PDF Download
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Author: Gabriel Navarro
Publisher: Cambridge University Press
ISBN: 1108428444
Category : Mathematics
Languages : en
Pages : 253
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Book Description
Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.
Author: Gabriel Navarro
Publisher: Cambridge University Press
ISBN: 1108428444
Category : Mathematics
Languages : en
Pages : 253
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Book Description
Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.
Author: Gabriel Navarro
Publisher: Cambridge University Press
ISBN: 110863172X
Category : Mathematics
Languages : en
Pages : 253
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Book Description
The McKay conjecture is the origin of the counting conjectures in the representation theory of finite groups. This book gives a comprehensive introduction to these conjectures, while assuming minimal background knowledge. Character theory is explored in detail along the way, from the very basics to the state of the art. This includes not only older theorems, but some brand new ones too. New, elegant proofs bring the reader up to date on progress in the field, leading to the final proof that if all finite simple groups satisfy the inductive McKay condition, then the McKay conjecture is true. Open questions are presented throughout the book, and each chapter ends with a list of problems, with varying degrees of difficulty.
Author: Meinolf Geck
Publisher: Cambridge University Press
ISBN: 1108808905
Category : Mathematics
Languages : en
Pages : 406
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Book Description
Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.
Author: Meinolf Geck
Publisher: Cambridge University Press
ISBN: 1108489621
Category : Mathematics
Languages : en
Pages : 405
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Book Description
A comprehensive guide to the vast literature and range of results around Lusztig's character theory of finite groups of Lie type.
Author: I. Martin Isaacs
Publisher: American Mathematical Soc.
ISBN: 1470434857
Category : Mathematics
Languages : en
Pages : 384
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Book Description
This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups. It is subdivided into three parts: -theory, character correspondences, and M-groups. The -theory section contains an exposition of D. Gajendragadkar's -special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included. Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.
Author: N.S. Narasimha Sastry
Publisher: Springer
ISBN: 9811320470
Category : Mathematics
Languages : en
Pages : 213
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Book Description
This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.
Author: Ted Dobson
Publisher: Cambridge University Press
ISBN: 1108429068
Category : Language Arts & Disciplines
Languages : en
Pages : 527
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Book Description
The first full-length book on the theme of symmetry in graphs, a fast-growing topic in algebraic graph theory.
Author: Jan van Neerven
Publisher: Cambridge University Press
ISBN: 1009232495
Category : Mathematics
Languages : en
Pages : 728
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Book Description
This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.
Author: Kiran S. Kedlaya
Publisher: Cambridge University Press
ISBN: 1009275658
Category : Mathematics
Languages : en
Pages : 518
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Book Description
Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations. The author includes many original results which play a key role in the study of $P$-adic geometry, crystalline cohomology, $P$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties. This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $P$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon.
Author: Francesco Maggi
Publisher: Cambridge University Press
ISBN: 1009179705
Category : Mathematics
Languages : en
Pages : 317
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Book Description
A pedagogical introduction to the key ideas and theoretical foundation of optimal mass transport for a graduate course or self-study.
