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Obtaining a unitary representation for a given group

Hans Dolhaine, retired
Posted 2 years ago

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Obtaining a unit...nb
POSTED BY: Hans Dolhaine
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This works because they commute

Table[gT[[i]] . gT[[j]] == gT[[j]] . gT[[i]], {i, 4}, {j, i, 4}]
POSTED BY: Mohammad Bahrami

Hello Dan. Strictly spoken I sum not over generators, but over the whole group. That is the trick that

Conjugate[T[a]] . H . T[a] equals H.

The details are outlined in the text cited.

Correction: it must be of course

TransposeConjugate[T[a]] . H . T[a] equals H.

POSTED BY: Hans Dolhaine

Nice. Thanks for sharing. BTW, one useful built-in function: UnitaryMatrixQ
POSTED BY: Mohammad Bahrami

Very nice. I have a question though. You create a new matrix by summing the generators and orthogonalize this new one. How do you know the transform will then simultaneously orthogonalize each summand? Does this come from the theory?
POSTED BY: Daniel Lichtblau

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