Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics)

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9780521415910: Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics)
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Schur algebras are an algebraic system that provide a link between the representation theory of the symmetric and general linear groups. Dr. Martin gives a self-contained account of this algebra and those links, covering the basic ideas and their quantum analogues. He discusses not only the usual representation-theoretic topics (such as constructions of irreducible modules, the structure of blocks containing them, decomposition numbers and so on) but also the intrinsic properties of Schur algebras, leading to a discussion of their cohomology theory. He also investigates the relationship between Schur algebras and other algebraic structures. Throughout, the approach uses combinatorial language where possible, thereby making the presentation accessible to graduate students. Some topics require results from algebraic group theory, which are contained in an appendix.

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The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it will be of interest to all research workers in representation theory.

Review:

"this book can be a source of useful information for beginners in the field of representations of symmetric and general linear groups and finite-dimensional algebras and specialists as well. Most of the treatments are combinatorial, so it is accessible to graduate students...the text is comprehensible and the research area is important and active...the book is readable and will be a handy book for specialists whose interests lie in this area." Jie Du, Mathematical Reviews

"An excellent and thorough survey of one of the currently liveliest topics in algebra. Congratulations for work well done, Mr, Martin." The Bulletin of Mathematics

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9780521100465: Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics)

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Publisher: Cambridge University Press, 2009
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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2007. Hardback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****. The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it will be of interest to all research workers in representation theory. Seller Inventory # APC9780521415910

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2007. Hardback. Condition: New. Language: English . Brand New Book ***** Print on Demand *****.The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it will be of interest to all research workers in representation theory. Seller Inventory # APC9780521415910

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