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The theory of linear algebraic groups has developed significantly since its beginnings in the 1950s and 1960s. Algebraic groups have many applications, including to Lie algebras, algebraic geometry, arithmetic geometry and number theory. The description of the irreducible representations of simple algebraic groups in terms of highest weights has become a paradigm for the representation theory of many other algebraic objects.

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Introduction

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  • 发表日期：

    2026年

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  • Michael Bate,
  • Benjamin Martin,
  • Gerhard Röhrle

摘要

The theory of linear algebraic groups has developed significantly since its beginnings in the 1950s and 1960s. Algebraic groups have many applications, including to Lie algebras, algebraic geometry, arithmetic geometry and number theory. The description of the irreducible representations of simple algebraic groups in terms of highest weights has become a paradigm for the representation theory of many other algebraic objects.