On representations of Lie algebras compatible with a grading

Miloslav Havlíček; Edita Pelantová; Jiří Tolar

On representations of Lie algebras compatible with a grading

Mathematical Physics 2010-11-16 v1 math.MP

Authors: Miloslav Havlíček , Edita Pelantová , Jiří Tolar

Abstract

The paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is defined and applied to finite-dimensional representations of $sl(n,\mathbb{C})$ in relation with its $\mathbb{Z}_2$ -gradings. For representation theory of $sl(n,\mathbb{C})$ the Gel'fand-Tseitlin method turned out very effective.

Keywords

Lie algebra representation grading compatible representation sl(n,C) Gelfand-Tseitlin method

Cite

@article{arxiv.0901.2300,
  title  = {On representations of Lie algebras compatible with a grading},
  author = {Miloslav Havlíček and Edita Pelantová and Jiří Tolar},
  journal= {arXiv preprint arXiv:0901.2300},
  year   = {2010}
}

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15 pages

On representations of Lie algebras compatible with a grading

Abstract

Keywords

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