'We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own' - from the Preface. Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, it has been one of the great tools in the study and classification of finite groups. The theory contains some particularly beautiful results: Frobenius' theorem, Burnside's theorem, Artin's theorem, Brauer's theorem - all of which are covered in this textbook. Some seem uninspiring at first but prove to be quite useful. Others are clearly deep from the outset.And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers.The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.
Simon P. Norton The uniqueness of the Fischer-Griess Monster Edmund F. Robertson Efficiency of finite simple groups and their covering groups Mark A. Ronan Buildings and sporadic groups Stephen D. Smith On the Head characters of the ...
Quan shu zhu yao nei rong bao kuo:qun lun de ji ben gai nian, Zhi huan qun, p qun he mi ling qun, Ke jie qun, Qun zai pei ji he qun shang de zuo yong, Hu su zuo yong he er ci zuo yong, You xian qun de ju bu he zheng ti de dui ying deng.
Any Markov kernel defines variables with values in V such a Markov that the chain following {Xn identity } ∞ n=0 as a sequence of random holds P(X n+1 = y | X n = x) = P (x, y), (1.5) and that the behavior of the process at any time n ...
This volume contains papers presented at a conference held in April 2007 at the CRM in Montreal honouring the remarkable contributions of John McKay over four decades of research.
Mathematical Surveys and Monographs
This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and ...
... Multiple Hilbert Transforms Associated with Polynomials, 2015 R. Bruggeman, J. Lewis, and D. Zagier, Period Functions for Maass Wave Forms and Cohomology, 2015 Chih-Yun Chuang, Ting-Fang Lee, Fu-Tsun Wei, and Jing Yu, Brandt Matrices ...
This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas.