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Unitary Reflection Groups: 20 (Australian Mathematical Society Lecture Series, Series Number 20) - Softcover
Synopsis
A complete and clear account of the classification of unitary reflection groups, which arise naturally in many areas of mathematics.
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About the Authors
Gustav I. Lehrer is a Professor in the School of Mathematics and Statistics at the University of Sydney.
Donald E. Taylor is an Associate Professor in the School of Mathematics and Statistics at the University of Sydney.
"About this title" may belong to another edition of this title.
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Unitary Reflection Groups
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Cambridge University Press, 2009
ISBN 10: 0521749891
ISBN 13: 9780521749893
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Unitary Reflection Groups (Australian Mathematical Society Lecture, 20).
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ISBN 13: 9780521749893
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Broschur, Gr.-8°. Condition: Gut. Illustrated. 304 S. Das Buch ist in sehr gutem, sauberen Zustand. Ecken und Kanten minimal bestossen. Sonst sauberes und wohlerhaltenes Exemplar. -----Inhalt:. This book provides a complete classification of unitary reflection groups - which arise naturally in many areas of mathematics. Designed for graduate students, but also suitable for researchers in algebra, topology and mathematical physics.A complex reflection is a linear transformation which fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or arrangement of mirrors. This book gives a complete classification of all groups of transformations of n-dimensional complex space which are generated by complex reflections, using the method of line systems. In particular: irreducible groups are studied in detail, and are identified with finite linear groups; reflection subgroups of reflection groups are completely classified; the theory of eigenspaces of elements of reflection groups is discussed fully; 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. Introduction; 1. Preliminaries; 2. The groups G(m, p, n); 3. Polynomial invariants; 4. Poincaré series and characterisations of reflection groups; 5. Quaternions and the finite subgroups of SU2(C); 6. Finite unitary reflection groups of rank two; 7. Line systems; 8. The Shepherd and Todd classification; 9. The orbit map, harmonic polynomials and semi-invariants; 10. Covariants and related polynomial identities; 11. Eigenspace theory and reflection subquotients; 12. Reflection cosets and twisted invariant theory; A. Some background in commutative algebra; B. Forms over finite fields; C. Applications and further reading; D. Tables; Bibliography; Index of notation; Index. ISBN: 9780521749893 Due to new EU packaging regulations, we are currently unable to ship to many EU countries. Shipping to Germany, the Netherlands, Ireland, Finland, and the Baltic states is possible. Deliveries to border-based parcel lockers or cross-border parcel forwarding services remain possible. Shipping to all countries outside the EU also remains possible. Sprache: Englisch Gewicht in Gramm: 431. Seller Inventory # 669033
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Unitary Reflection Groups
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ISBN 13: 9780521749893
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Unitary Reflection Groups
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ISBN 13: 9780521749893
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Unitary Reflection Groups (Australian Mathematical Society Lecture Series, Series Number 20)
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Unitary Reflection Groups (Paperback)
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Paperback. Condition: new. Paperback. A complex reflection is a linear transformation which fixes each point in a hyperplane. Intuitively, it resembles the transformation an image undergoes when it is viewed through a kaleidoscope, or arrangement of mirrors. This book gives a complete classification of all groups of transformations of n-dimensional complex space which are generated by complex reflections, using the method of line systems. In particular: irreducible groups are studied in detail, and are identified with finite linear groups; reflection subgroups of reflection groups are completely classified; the theory of eigenspaces of elements of reflection groups is discussed fully; 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. This book provides a complete classification of unitary reflection groups which arise naturally in many areas of mathematics. Designed for graduate students, but also suitable for researchers in algebra, topology and mathematical physics. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9780521749893
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Unitary Reflection Groups (Australian Mathematical Society Lecture Series)
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ISBN 13: 9780521749893
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