Group Matrices, Group Determinants and Representation Theory
The Mathematical Legacy of Frobenius
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Beschreibung
This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science.
The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science.
The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.The simple tools described provide a new way of looking at group representation theory and its applications Offers an insight into the mind of one of the great mathematicians Much of the work described has not previously appeared in book form
Autor*in
Kenneth W. Johnson
Themen in »Group Matrices, Group Determinants and Representation Theory«
Group Determinant Group Matrix k-Characters of Groups Norm forms on algebras Association schemes S-rings Fusion of characters Fission of characters Weak Cayley table Fourier transforms Random walks combinatorics
Stimmen zu »Group Matrices, Group Determinants and Representation Theory«
“The book is clearly written and presents many little known facts about group matrices. No other book deals so thoroughly with this topic.” (John D. Dixon, zbMATH 1458.20001, 2021)
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