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Example 1.
We define a representation and make a change of basis for the representation space.
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| (2.1) |
Alg1 >
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Define the new basis for the representation space.
Alg1 >
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| (2.4) |
Compute the representation in the basis B.
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We can use the Query command to check that is a representation of Alg1.
Alg1 >
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Check, by example, that the matrices for are correct. We apply rho(e1) to Fr[1] and express the result as a linear combination of the vectors Fr. This should give the first column of the matrix for e1 in phi1.
Alg1 >
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Example 2.
We obtain the same change of basis as in Example 1 using the other calling sequence for the procedure ChangeRepresentationBasis. We take the matrix A to be the matrix whose columns are the coefficients of the new basis in terms of the old.
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Example 3.
Now we make a change of basis in the Lie algebra. First we use the LieAlgebraData command to create the Lie algebra in the new basis.
Alg1 >
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| (2.10) |
Alg1 >
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| (2.11) |
Alg1 >
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Alg2 >
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Alg2 >
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Example 4. We obtain the same change of basis as in Example 3 using the other calling sequence for the procedure ChangeRepresentationBasis. We take the matrix A to be the matrix whose columns are the coefficients of the new basis in terms of the old.
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Alg1 >
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Alg1 >
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