Weyl module
E1576273
UNEXPLORED
A Weyl module is a finite-dimensional highest-weight representation of a semisimple Lie algebra (or algebraic group) that plays a central role in the classification and study of their representations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Weyl module canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T23235057 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl module Context triple: [Verma module, relatedConcept, Weyl module]
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A.
Verma module
A Verma module is a type of highest-weight module over a Lie algebra that is freely generated from a highest-weight vector and plays a central role in the classification of representations of semisimple Lie algebras.
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B.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
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C.
Weyl dimension formula
The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
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D.
Weyl vector
The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
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E.
Weyl denominator
The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weyl module Target entity description: A Weyl module is a finite-dimensional highest-weight representation of a semisimple Lie algebra (or algebraic group) that plays a central role in the classification and study of their representations.
-
A.
Verma module
A Verma module is a type of highest-weight module over a Lie algebra that is freely generated from a highest-weight vector and plays a central role in the classification of representations of semisimple Lie algebras.
-
B.
Weyl character formula
The Weyl character formula is a fundamental result in representation theory that gives an explicit expression for the characters of irreducible finite-dimensional representations of semisimple Lie algebras and Lie groups.
-
C.
Weyl dimension formula
The Weyl dimension formula is a fundamental result in representation theory that gives an explicit product expression for the dimension of each finite-dimensional irreducible representation of a semisimple Lie algebra or compact Lie group in terms of its highest weight and the root system.
-
D.
Weyl vector
The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
-
E.
Weyl denominator
The Weyl denominator is a key product expression in Lie theory that appears in the Weyl character formula, encoding the alternating sum over the Weyl group and playing a central role in describing characters of irreducible representations of semisimple Lie algebras.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.