Weight zero in tensor-decomposable irreducible representations of simple algebraic groups

[摘要] Let G be a simple algebraic group in defining characteristic p > 0, and let V be an irreducible G-module which is the tensor product of exactly two non-trivial modules. We obtain a criterion for V to have the zero weight. In addition, we provide a uniform criterion for an irreducible representation of a simple Lie algebra over the complex numbers to have a multiple of a prescribed fundamental weight. (c) 2021 Elsevier B.V. All rights reserved.

[发布日期] 2021-12-01

[关键词] Simple algebraic group;Modular representations;Weight 0