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Decomposition of tensor spaces into irreducible tensor subspaces


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  • Product Description

The work is organized as follows: We give basic definitions from group theory and group representations, with some examples. We represent all the irreducible representations of the symmetry group S(n), we define the notion of the Young diagram and show that the number of inequivalent irreducible representation of S(n) is the same as the number of different Young diagrams. We also define the Hook formula for dimensions. We give a background of algebraic material and define the Young symmetrizer operator. We give a brief introduction to tensor algebra. In order to clarify the relation between the group GL(V) (in this paper we concentrate on the group S(n)GL(V)) and the tensor space we give an alternative definition of the tensor space T^(n)(V) as C[S(n)]-Module. The standard tableau are defined and the corresponding decomposition of the tensor space is given. We decompose the spaces T^(2)(V); T^(3)(V) and T^(4)(V). We decompose the tensor spaces for n = 2; 3; 4 according to the subgroup O(n) of GL(V). In this work we are dealing with a "bare" vector space. Our main aim is to study the irreducible tensor decompositions of vector spaces with additional structures.

Product Specifications
SKU :COC24773
AuthorOphir Nave
Number of Pages64
Publishing Year10/16/2012
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-28 00:00:00