Please let me know if you find errors or typos! Here are the ones that I'm aware of. (Special thanks to Max Horn and his group, and to Shlomo Sternberg, for pointing out errors.)
• P. xx (list of symbols): corrot lattice'' should read coroot lattice''.
• p.2, Proposition 1.1: remove "or $\mathbb{Q}$" from the statement and proof; for $\mathbb{Q}$ the claim that one can always normalize the vectors to have $B(E_i,E_i)=\pm 1$ is false, in general.
• p.5, bottom of page: maps whose kernel and range are in $F$'' should read maps vanishing on $F$ and with range in $F$''.
• p.9, top of page: Hence R_1R_2-R_2R_1'' should read Hence R_1R_2=R_2R_1''.
• p. 29, top: One should state clearly that $I\subseteq \{1,\ldots,n\}$ is an ordered subset, i.e., $i_1 < i_2 < \cdots$.
• p.42, before Prop. 2.14: is a polynomial of degree $k$'' -- one should say more clearly, is a homogeneous polynomial of degree $k$''. (Alse elsewhere in this section.)
• p.43, in Prop. 2.14: A factor of $1/k!$ is missing on the right hand side.
• p. 43: Proof of Prop. 2.14: ... depends only the '' should read ... depends only on the ''.
• p. 44: $C^\infty(M)$ should read $C^\infty(Q)$
• p. 51, in the formula for $A_x(f)$, replace the final "e" by "f".
• p. 63, in the middle of the proof of Theorem 3.6, replace $\bigcap_{v\in V}$ with $\bigcap_{v\in F}$ (twice).
• p. 66, three lines above Def. 3.6, replace $K_{S^F}$ with $K_{S_F}$.
• p. 66, Proposition 3.13, displayed equation: Remove subscripts $S$ from the pairings.
• p.68, line -6: Replace $\mu_1,\mu_2$ with $\mu^1,\mu^2$.
• p.98, first displayed formula in proof: $(I + DE_1)T$ should read $(I + E_1D)T$.
• p.99, first displayed formula of section 4.3.2.: $B^\flat\circ g(A)$ should read $g(A)\circ B^\sharp$.
• p.100, after Theorem 4.2: In the sentence Once again, while'' skip Once again''. The phrase below'' refers to Theorem 4.4.
• p.123, middle of proof of Lemma 5.3: for $k\neq 0$ '' should read for $k\neq 1$ ''.
• p.150, first displayed formula: $L(\xi)$ should read $L_\wedge(\xi)$ .
• p.165, beginning of proof: By applying the operator $\exp(-\frac{1}{2} \sum_a [..])$'' omit the $\frac{1}{2}$.
• p.168, beginning of proof: degree 2'' should read degree 3''.
• p.169, second displayed line from bottom: The plus sign should be a minus sign.
• p.200, bottom of page: $w\mathfrak{t}_+\supseteq \mathfrak{t}_{\mathfrak{k},+}$ should read $w\mathfrak{t}_+\subseteq \mathfrak{t}_{\mathfrak{k},+}$
• p.204, displayed formula after (8.9): The middle equation should read $.. (V\otimes \mathsf{S}_{\mathfrak{p}}^{\bar{1}})/\ \mathcal{D}_V (V\otimes \mathsf{S}_{\mathfrak{p}}^{\bar{0}})=..$
• p.205, Remark 8.10: triplets'' should read multiplets''.