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In the study of representation theory of semisimple Lie algebras, finding explicit descriptions of bases of irreducible representations is a fundamental problem. The notion of birational sequences and the associated essential monomials provide a systematic and algorithmic way of constructing such bases. In this chapter, we introduce the OSCAR package computing monomial bases of irreducible representations based on birational sequences.

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Monomial Bases in Lie Theory

  • 章节

  • 发表日期：

    2025年

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  • Xin Fang,
  • Ghislain Fourier

摘要

In the study of representation theory of semisimple Lie algebras, finding explicit descriptions of bases of irreducible representations is a fundamental problem. The notion of birational sequences and the associated essential monomials provide a systematic and algorithmic way of constructing such bases. In this chapter, we introduce the OSCAR package computing monomial bases of irreducible representations based on birational sequences.