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Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory.

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  • モジュラー表現論 (ja)
  • Modular representation theory (en)
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  • Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory. (en)
  • 数学の一分野としてのモジュラー表現論(モジュラーひょうげんろん、英: modular representation theory)は表現論の一部として、有限群 G の正標数の体 K 上での線型表現を研究する。群論への応用を持つのみならず、モジュラー表現論は代数幾何学、符号理論、組合せ論、数論など他の数学分野においても自然に生じてくる。 有限群論において、がモジュラー表現論を用いて証明した指標理論的な結果は、有限単純群の分類の過程で、特にそのシロー 2-群が適当な意味において小さすぎるために純群論的手法では従順でないと特徴付けられる単純群に対して、重要な役割を果たした。また、がブラウアーの展開した理論を用いて示した、有限群の位数 2 の元の埋め込みに関する一般的な結果は、と呼ばれ、分類を進めるうえで特に有効であった。 (ja)
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