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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 519=18, 2014.

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

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Abstract

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.

Keywords

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

Hrčak ID:

127646

URI

https://hrcak.srce.hr/127646

Publication date:

30.9.2014.

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