Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: symplectic group Sp(2n,ℝ) | Statement: [semisimple Lie group, hasExample, symplectic group Sp(2n,ℝ)]

Target entity: symplectic group Sp(2n,ℝ)
Context triple: [semisimple Lie group, hasExample, symplectic group Sp(2n,ℝ)]

• A. special orthogonal group SO(n)
  The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
• B. SL(2,R)
  SL(2,R) is the Lie group of 2×2 real matrices with determinant 1, fundamental in representation theory, geometry, and the study of symmetries in mathematics and physics.
• C. Spin(2,d)
  Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
• D. 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.
• E. metaplectic group
  The metaplectic group is a double cover of the symplectic group that plays a central role in number theory and representation theory, particularly through its connection to theta functions and automorphic forms.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: symplectic group Sp(2n,ℝ)
Target entity description: The symplectic group Sp(2n,ℝ) is the Lie group of 2n×2n real matrices that preserve a nondegenerate skew-symmetric bilinear form, playing a central role in symplectic geometry and Hamiltonian mechanics.

• A. special orthogonal group SO(n)
  The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
• B. SL(2,R)
  SL(2,R) is the Lie group of 2×2 real matrices with determinant 1, fundamental in representation theory, geometry, and the study of symmetries in mathematics and physics.
• C. Spin(2,d)
  Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
• D. 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.
• E. metaplectic group chosen
  The metaplectic group is a double cover of the symplectic group that plays a central role in number theory and representation theory, particularly through its connection to theta functions and automorphic forms.
• F. None of above.