On a Tensor Quantity Involved in Harish-Chandra Formula for the Product of Dirac-Matrices

Abstract

In his paper, Harish-Chandra gave the beautiful formula for the product of Dirac-matrices. His formula involves an anti-symmetric tensor quantity   in which each index takes the values from 0 to 5. Each non-zero component of this tensor depends on the permutation of the set {0, 1, 2, 3, 4, 5}. To understand the analysis given in Harish-Chandra it is essential to have an idea of such components of this tensor. For this purpose in this paper we have given a computer programme in ‘C’ language which first obtains all the permutations of the set {0, 1, 2, 3, 4, 5}, then arranges them in their increasing order, decides each whether it is an even or odd
permutation and then prints the non-zero components of  in the increasing order of their arguments. The output of the programme is also given.