What question did this study set out to answer?

To develop a method for constructing nontrivial homomorphisms between Verma modules of semisimple Lie algebras.

March 29, 2026Journal of Lie theoryOpen Access

Constructing Homomorphisms between Verma Modules

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To develop a method for constructing nontrivial homomorphisms between Verma modules of semisimple Lie algebras.
Described a practical construction method for homomorphisms
Focused on nontrivial homomorphisms between two Verma modules
Extended the method to affine Lie algebra cases
Presented a systematic approach to obtain homomorphisms
Showed the applicability of the method to affine cases
Demonstrated that the method works for arbitrary semisimple Lie algebras

Implication

Describes a method for constructing homomorphisms in Verma modules, indicating applications in broader algebraic structures.

Abstract

We describe a practical method for constructing a nontrivial homomorphism between two Verma modules of an arbitrary semisimple Lie algebra.With some additions the method generalises to the affine case.

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Cite This Study

W. A. d. Graaf (2005) studied this question.

synapsesocial.com/papers/69c8c15ade0f0f753b39bd2d https://doi.org/10.5802/jolt.383

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Implication

Describes a method for constructing homomorphisms in Verma modules, indicating applications in broader algebraic structures.

Constructing Homomorphisms between Verma Modules

Key Points

Implication

Abstract

Discussion

Cite This Study

Constructing Homomorphisms between Verma Modules

Key Points

Implication

Abstract

Discussion

Cite This Study

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