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The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor. The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53035144413457,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53035144904977,"sku":"NIN9780691027302","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691027302.jpg?v=1768746199"},{"product_id":"cohomology-of-quotients-in-symplectic-and-algebraic-geometry-book-frances-clare-kirwan-9780691083704","title":"Cohomology of Quotients in Symplectic and Algebraic Geometry","description":"These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties are interesting in particular because of their relevance to moduli problems in algebraic geometry. The author describes two different approaches to the problem. One is purely algebraic, while the other uses the methods of symplectic geometry and Morse theory, and involves extending classical Morse theory to certain degenerate functions.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53035153883409,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53035156406545,"sku":"NIN9780691083704","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691083704.jpg?v=1768746214"},{"product_id":"lectures-on-hermite-and-laguerre-expansions-book-sundaram-thangavelu-9780691000480","title":"Lectures on Hermite and Laguerre Expansions","description":"The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of Hermite, special Hermite, and Laguerre functions. The main thrust of the book is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems. The questions of almost-everywhere and mean convergence of Bochner-Riesz means are also treated. Most of the results in this monograph appear for the first time in book form.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53362522751249,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53362523341073,"sku":"NIN9780691000480","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691000480.jpg?v=1774991043"},{"product_id":"diffusion-quantum-theory-and-radically-elementary-mathematics-book-william-g-faris-9780691125459","title":"Diffusion, Quantum Theory, and Radically Elementary Mathematics","description":"Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53381304287505,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53381304680721,"sku":"NIN9780691125459","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691125459.jpg?v=1775525201"}],"url":"https:\/\/www.worldofbooks.com\/en-ie\/collections\/mathematical-notes-book-series.oembed","provider":"World of Books ","version":"1.0","type":"link"}