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Original scientific paper

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

Zlatko Drmač ; Faculty of Sciences, Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia
Tomislav Šikić ; Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, Croatia

Full text: english pdf 248 Kb

page 55-72

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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.


Z-gradation for classical (affine) Lie algebra, Kac parameters of finite order automorphisms of simple Lie algebras, matrix of specialized roots, integer skew-symmetric matrix, spectral decomposition

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