Normalizers, Weyl Groups
We saw in Chapter X that Sp(1) ≅ Spin(3) and Sp(2) ≅ Spin(5) (also that Spin(6) ≅ SU(4)). The only remaining question in our isomorphism puzzle is whether Sp(k) and Spin(2k+1) are isomorphic for k ≥ 3. In this chapter, we will use normalizers and Weyl groups to show that they are not.
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