{"product_id":"unitary-reflection-groups-paperback-9780521749893","title":"Unitary Reflection Groups (Paperback) 9780521749893","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eUnitary Reflection Groups\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA complete and clear account of the classification of unitary reflection groups, which arise naturally in many areas of mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eGustav I. Lehrer (Author), Donald E. Taylor (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521749893, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 13 August 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e302 pages, 12 tables  110 exercises\u003cbr\u003e22.8 x 15.2 x 1.6 cm, 0.44 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eA 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. Preliminaries\u003cbr\u003e 2. The groups G(m, p, n)\u003cbr\u003e 3. Polynomial invariants\u003cbr\u003e 4. Poincaré series and characterisations of reflection groups\u003cbr\u003e 5. Quaternions and the finite subgroups of SU2(C)\u003cbr\u003e 6. Finite unitary reflection groups of rank two\u003cbr\u003e 7. Line systems\u003cbr\u003e 8. The Shepherd and Todd classification\u003cbr\u003e 9. The orbit map, harmonic polynomials and semi-invariants\u003cbr\u003e 10. Covariants and related polynomial identities\u003cbr\u003e 11. Eigenspace theory and reflection subquotients\u003cbr\u003e 12. Reflection cosets and twisted invariant theory\u003cbr\u003e A. Some background in commutative algebra\u003cbr\u003e B.  Forms over finite fields\u003cbr\u003e C. Applications and further reading\u003cbr\u003e D. Tables\u003cbr\u003e Bibliography\u003cbr\u003e Index of notation\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Algebra [\u003ca title=\"See our other books on Algebra\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebra%20%5BPBF%5D%22\"\u003ePBF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46005332082968,"sku":"9780521749893","price":63.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521749893i_4406a7bd-21e3-4711-8a30-15e41a1f4324.jpg?v=1691380748","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/unitary-reflection-groups-paperback-9780521749893","provider":"Freshly Printed Books","version":"1.0","type":"link"}