On Kac parameters and spectral decomposition of a matrix of specialized roots of Lie algebra sl_n

This paper presents interesting spectral properties of a particular integer skew-symmetric matrix, used to encode information on Z-gradation of type ˜s for classical affine Lie algebra ˜sl_n. It is shown that the hidden Kac parameters can be revealed using an explicitly computed eigenvector in a Gram-Schmidt orthogonalization process