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- TL;DR Summary
- Defining the special unitary group independent of matrix representation

In matrix representation, the special unitary group is distinguished from the more general unitary group by the sign of the matrix determinant. However, this presupposes that the special unitary group is formulated in matrix representation. For a unitary group action NOT formulated in matrix representation, what differentiates a special unitary group action from a more general unitary group action, such as in the infinite dimensional case?