Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications

preview-18
  • Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications Book Detail

  • Author : Alexey P Isaev
  • Release Date : 2020-07-16
  • Publisher : World Scientific
  • Genre : Science
  • Pages : 615
  • ISBN 13 : 9811217424
  • File Size : 78,78 MB

Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications by Alexey P Isaev PDF Summary

Book Description: 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.

Disclaimer: www.yourbookbest.com does not own Theory Of Groups And Symmetries: Representations Of Groups And Lie Algebras, Applications books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Vortex Atom, The: A New Paradigm

Vortex Atom, The: A New Paradigm

File Size : 14,14 MB
Total View : 5917 Views
DOWNLOAD

With clear illustrations throughout and without recourse to quantum mechanics, the reader is invited to revisit unsolved problems lying at the foundations of th

New Perspectives On Einstein's E = Mc2

New Perspectives On Einstein's E = Mc2

File Size : 40,40 MB
Total View : 780 Views
DOWNLOAD

Einstein's energy-momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of