GL_n(Q_l)
E1495485
UNEXPLORED
GL_n(Q_l) is the group of invertible n×n matrices over the field of ℓ-adic numbers, fundamental in the study of ℓ-adic Galois representations and arithmetic geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| GL_n(Q_l) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T21654185 — 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: GL_n(Q_l) Context triple: [Galois representations, typicalCodomain, GL_n(Q_l)]
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A.
general linear group GL(n,R)
The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
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B.
general linear group GL(n,C)
The general linear group GL(n,ℂ) is the Lie group consisting of all invertible n×n complex matrices under matrix multiplication, fundamental in linear algebra and representation theory.
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C.
special linear group SL(n,R)
The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
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D.
special linear group SL(n,C)
The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
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E.
Weil–Deligne group
The Weil–Deligne group is an extension of the Weil group by a copy of the additive group that encodes both arithmetic and monodromy data, playing a central role in the local Langlands correspondence and the study of l-adic Galois representations.
- 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: GL_n(Q_l) Target entity description: GL_n(Q_l) is the group of invertible n×n matrices over the field of ℓ-adic numbers, fundamental in the study of ℓ-adic Galois representations and arithmetic geometry.
-
A.
general linear group GL(n,R)
The general linear group GL(n,ℝ) is the Lie group consisting of all invertible n×n real matrices under matrix multiplication, fundamental in linear algebra and differential geometry.
-
B.
general linear group GL(n,C)
The general linear group GL(n,ℂ) is the Lie group consisting of all invertible n×n complex matrices under matrix multiplication, fundamental in linear algebra and representation theory.
-
C.
special linear group SL(n,R)
The special linear group SL(n,ℝ) is the Lie group of all n×n real matrices with determinant 1, fundamental in linear algebra and differential geometry as the group of volume-preserving linear transformations.
-
D.
special linear group SL(n,C)
The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
-
E.
Weil–Deligne group
The Weil–Deligne group is an extension of the Weil group by a copy of the additive group that encodes both arithmetic and monodromy data, playing a central role in the local Langlands correspondence and the study of l-adic Galois representations.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.