Decomposition of tensor spaces into irreducible tensor subspaces: An explicit formula of decomposition of the tensor spaces into subspace with trace zero - Softcover

Nave, Ophir

Softcover

ISBN 10: 365927366X ISBN 13: 9783659273667

Publisher: LAP LAMBERT Academic Publishing, 2012

Synopsis

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.

About this title

About the Author

Ophir Nave education: Ph.D. 2010, Applied Mathematics, Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Israel.Advisor: Prof. V. Gol'dshtein.M.Sc. 2005, Mathematics-Physics, Department of mathematics, The Hebrew University of Jerusalem.Advisors: Prof. Shmuel Kaniel and Dr. Ya'akov Itin.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2012
• ISBN 10: 365927366X
• ISBN 13: 9783659273667
• Binding: Paperback
• Language: English
• Number of pages: 64