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In his 1939 book Weyl indeed did not use the notation SO but $O^+$, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

The name "special unitary group" does not appear, it is always "unimodular".

The footnote on the name "symplectic group", from the same book, is amusing:

In his 1939 book Weyl indeed did not use the notation SO but $O^+$, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

The name "special unitary group" does not appear, it is always "unimodular".

The footnote on the name "symplectic group", from the same book, is amusing:

In his 1939 book Weyl indeed used $O^+$ instead of SO, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

The name "special unitary group" does not appear, it is alsways "unimodular".

The footnote on the name "symplectic group", from the same book, is amusing:

In his 1939 book Weyl indeed did not use the notation SO but $O^+$, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

The name "special unitary group" does not appear, it is always "unimodular".

The footnote on the name "symplectic group", from the same book, is amusing:

In his 1939 book Weyl indeed used $O^+$ for SO, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

The name "special unitary group" does not appear, it is alsways "unimodular".

In his 1939 book Weyl indeed used $O^+$ instead of SO, and called it the proper orthogonal group, but he did use the notation SU, or more precisely $^s$U with a tiny superscript s.

The name "special unitary group" does not appear, it is alsways "unimodular".

The footnote on the name "symplectic group", from the same book, is amusing: