Symplectic Representation
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ) which preserves the symplectic form . Here is a nondegenerate skew symmetric bilinear formIf G is a compact group (for example, a finite group), and F is the field of complex numbers, then by introducing a compatible unitary structure (which exists by an averaging argument), one can show that any complex symplec...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ) which preserves the symplectic form . Here is a nondegenerate skew symmetric bilinear formIf G is a compact group (for example, a finite group), and F is the field of complex numbers, then by introducing a compatible unitary structure (which exists by an averaging argument), one can show that any complex symplectic representation is a quaternionic representation. Quaternionic representations of finite or compact groups are often called symplectic representations, and may be identified using the Frobenius-Schur indicator.
