### Errata

(Last update: 8/25/17)

• §4.1, p.15: The assertion that $i\ell$, $j\ell$, $k\ell$ square to $-1$ does not follow from the assumptions so far. See the updates page for further discussion.
• §6.4, p.38: The assertion in (6.29) that $SO4^\pm\cong\SO(3)$ and in (6.32) that $\SO(3)\times\SO(3)=\SO(4)$ are only true locally, not globally. The correct assertions are that $SO4^\pm\cong\SU(2)$ and that $\SO(3)\times\SO(3)$ is the factor group of $\SO(4)$ by its reflection subgroup.
• §9.4, p.74: Contrary to the stated assertion, it was not shown in §8.1 that $\Sp(2)\cong\Spin(5)$. Further discussion can be found on the updates page.
• §13.5.3, p.154: The last component in the matrix in (13.133) is incorrectly typeset, and should be $p$. The correct equation is:

\CCC = \begin{pmatrix} p & iq & -q(j-i\ell-j\ell) \\ \noalign{\smallskip} -iq & p & q(1+k+l) \\ \noalign{\smallskip} q(j-i\ell-j\ell) & -q(1-k-l) & p \\ \end{pmatrix}

• §10.3, p.81: The caption of Figure 10.1 lists the root diagrams in the wrong order. The correct order is $\dd_2=\so(4)$, $\aa_2=\su(3)$, $\bb_2=\so(5)$, $\gg_2$, that is, $\aa_2$ and $\bb_2$ have been swapped. Furthermore, the diagram labeled $\bb_2$ is usually associated with $\cc_2=\sp(2)$, although these Lie algebras (and their root diagrams) are isomorphic.
• §14.1, p.164: The footnote should say “$2\hbar^2$” times the identity.