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LieAlgebras[SubRepresentation] - find the induced representation on an invariant subspace of the representation space
Calling Sequences
SubRepresentation(rho, S, W)
Parameters
rho - a representation of a Lie algebra g on a vector space V
S - a list of vectors in V whose span defines a rho invariant subspace of V
W - a Maple name or string, giving the frame name for the representation space for the subrepresentation
Description
If rho: g -> gl(V) is a representation and S is a subspace of V, then S is rho invariant if rho(x)(y) in S for all x in g and y in S. The command SubRepresentation(rho, W) returns the representation phi of g on the vector space S defined by phi(x)(y) = rho(x)(y) for all x in g and y in S.
Examples
Example 1.
We shall define a 4-dimensional representation rho of a 4 dimensional Lie algebra taken from the DifferentialGeometry Library, find an invariant subspace S of rho, and calculate the subrepresentation of rho on S.
Initialize the Lie algebra Alg1.
Initialize the representation space V.
Define the Matrices which specify a representation of Alg1 on V.
Define the representation with the Representation command.
Define a subspace of V.
We can use the Query command to check that S is a rho invariant subspace.
Define a frame for the induced representation of rho on S.
See Also
DifferentialGeometry, Library, LieAlgebras, Query, Representation, Retrieve
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