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Khovanov-Lauda-Rouquier algebras of finite Lie type come with families ofstandard modules, which under the Khovanov-Lauda-Rouquier categorificationcorrespond to PBW-bases of the positive part of the corresponding quantizedenveloping algebra. We show that there are no non-zero homomorphisms betweendistinct standard modules and all non-zero endomorphisms of a standard moduleare injective. We obtain applications to extensions between standard modulesand modular representation theory of KLR algebras.

Homomorphisms between standard modules over finite type KLR algebras