Using the bounded functional calculus, one can prove part of the Stone's theorem on one-parameter unitary groups:
32.
Unitary designs are analogous to spherical designs in that they approximate the entire unitary group via a finite collection of unitary matrices.
33.
The problem thus becomes classifying two jointly irreducible one-parameter unitary groups and which satisfy the Weyl relation on separable Hilbert spaces.
34.
In modern terms, this presents the special unitary group SU ( 2 ) as a double cover of SO ( 3 ).
35.
Recently it has been shown that the image of the Lawrence Krammer representation is dense subgroup of the unitary group in this case.
36.
The group manifold is not compact; rather its maximal compact subgroup is the unitary group U ( " n " ).
37.
There is another infinite-dimensional unitary group, of major significance in homotopy theory, that to which the Bott periodicity theorem applies.
38.
The PSU obviously refers to the projective special unitary group . . . but I am only familiar with this over the complex numbers.
39.
Moreover the subgroup commuting with " J " is naturally identified with the unitary group for the corresponding complex inner product space.
40.
The center of the special unitary group has order and consists of those unitary scalars which also have order dividing " n ".
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