Theory of Groups and Symmetries Representations of Groups and Lie Algebras Applications is popular PDF and ePub book, written by Alexey P. Isaev in 2020-07-13, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, Theory of Groups and Symmetries Representations of Groups and Lie Algebras Applications can be Read Online from any device for your convenience.
Theory of Groups and Symmetries Representations of Groups and Lie Algebras Applications Book PDF Summary
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras. The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed. Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed. Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Detail Book of Theory of Groups and Symmetries Representations of Groups and Lie Algebras Applications PDF
- Author : Alexey P. Isaev
- Release : 13 July 2020
- Publisher : World Scientific Publishing Company
- ISBN : 9811217408
- Genre : Science
- Total Page : 500 pages
- Language : English
- PDF File Size : 21,6 Mb
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