# Group Theory and Unitary Symmetry[MatSciRep:61]

 dc.contributor.author Santhanam, T.S. dc.date.accessioned 2010-09-03T06:19:16Z dc.date.available 2010-09-03T06:19:16Z dc.date.issued 2010-09-03T06:19:16Z dc.date.submitted 1968 dc.identifier.uri http://hdl.handle.net/123456789/228 dc.description.abstract The introductory chapter on Elementary particles gives an account of Interaction between particles, like Electromagnetic interaction, Strong interactions, weak interactions and it also reviews the Dirac Equation. This report deals with Group Theory, Lie Algebra, Lie Groups, Classical Groups, Root Structure, Representations of Lie Group and Lie Algebras and Unitary Groups. The report also talks about 'Discrete Transformation', where CPT and their Implications and Reactions are described and definitions of Conjugation is given. In the chapter "Generating functions of classical groups and evaluation of partition functions", the concepts like properties of simple reducibility, Equivalence of an irreducible representation and its conjugates, multiplicity, internal multiplicity structure are discussed. Recursion relations for the internal multiplicity is obtained. The general discussion of 'Kostant's formula', the Weyl group, the structure of positive and primitive roots, and the diophantine equations are dealt with. Conclusion: The Generating function for various classical groups have been constructed which are then used to set up recursion relations for the partition function which enter the Kostant's formula for the inner multiplicity structure. The essential idea of the whole analysis is the realization that the number of solutions of the matrix equation K = Ca ( for given k and c) where the matrix C is in general a rectangular matrix with non-negative integer coefficients, and the components of the vectors k and a are again non-negative integers, given by the coefficients of x1^k1, ... xl^kl of the generating function. The connection between the internal and external multiplicity structures are also discussed. en_US dc.subject Group Theory en_US dc.subject Unitary Symmetries en_US dc.subject Matscience Report 61 en_US dc.title Group Theory and Unitary Symmetry[MatSciRep:61] en_US dc.type.institution Institute of Mathematical Sciences en_US dc.description.pages 23; 38; 23p. en_US dc.type.mainsub Mathematics en_US

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