Intersection Multiplicities and Reflection Subquotients of Unitary Reflection Groups
Author : G. I. Lehrer
Publisher :
Page : pages
File Size : 47,45 MB
Release : 1996
Category :
ISBN :
Intersection Multiplicities and Reflection Subquotients of Unitary Reflection Groups I
Author : G. I. Lehrer
Publisher :
Page : 15 pages
File Size : 24,60 MB
Release : 1996
Category : Intersection theory
ISBN :
Book Description
Unitary Reflection Groups
Author : Gustav I. Lehrer
Publisher : Cambridge University Press
Page : 303 pages
File Size : 19,74 MB
Release : 2009-08-13
Category : Mathematics
ISBN : 0521749891
Book Description
A unitary reflection is a linear transformation of a complex vector space that fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or an arrangement of mirrors. This book gives a complete classification of all finite groups which are generated by unitary reflections, using the method of line systems. Irreducible groups are studied in detail, and are identified with finite linear groups. The new invariant theoretic proof of Steinberg's fixed point theorem is treated fully. The same approach is used to develop the theory of eigenspaces of elements of reflection groups and their twisted analogues. This includes an extension of Springer's theory of regular elements to reflection cosets. An appendix outlines links to representation theory, topology and mathematical physics. Containing over 100 exercises, ranging in difficulty from elementary to research level, this book is ideal for honours and graduate students, or for researchers in algebra, topology and mathematical physics. Book jacket.
Geometric Group Theory Down Under
Author : John Cossey
Publisher : Walter de Gruyter
Page : 349 pages
File Size : 15,72 MB
Release : 2011-05-02
Category : Mathematics
ISBN : 311080686X
Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
New Developments in Singularity Theory
Author : Dirk Siersma
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 14,97 MB
Release : 2001-06-30
Category : Mathematics
ISBN : 9780792369967
Book Description
Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.
Current Developments in Mathematics
Author :
Publisher :
Page : 304 pages
File Size : 34,32 MB
Release : 2000
Category : Mathematics
ISBN :
Book Description
Proceedings of the International Congress of Mathematicians: Invited lectures
Author : Gerd Fischer
Publisher :
Page : 904 pages
File Size : 21,90 MB
Release : 1998
Category : Mathematics
ISBN :
Book Description
Atti Del ... Congresso Internazionale Dei Matematici ...
Author :
Publisher :
Page : 904 pages
File Size : 21,70 MB
Release : 1998
Category : Mathematics
ISBN :
Book Description
Mathematical Reviews
Author :
Publisher :
Page : 764 pages
File Size : 31,22 MB
Release : 2000
Category : Mathematics
ISBN :
Book Description
Reflection Groups and Coxeter Groups
Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 222 pages
File Size : 13,4 MB
Release : 1992-10
Category : Mathematics
ISBN : 9780521436137
Book Description
This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.
