TITLE: Erratum for Fulton and Harris
QUESTION [14 upvotes]: I am currently using Fulton and Harris for a course on representation theory, and I have noticed that there are a few errors throughout the book. A search on google with the keywords "Errata for Fulton and Harris" doesn't come up with anything. 
I believe the book is widely used in many representation theory courses, and it would be helpful if a list of errata could be compiled. Does anyone know of any list of errata for this?
Thanks.
Errors I have found: On page 150 (in the middle) the line "...so the representation $W = \Bbb{C}\cdot x^2 \oplus \Bbb{C} \cdot xy \oplus \Bbb{C} \cdot y^2 = W_{-2} \oplus W_0 \otimes W_2$ is the..." should have a direct sum in place of tensor product in between $W_0$ and $W_2$.

REPLY [3 votes]: I may have found another error. In exercise 14.37, they ask to show that the Killing Form on $SO(n,\mathbb{R})$ is positive definite. But the formula for the Killing form on the underlying Lie algebra, which is $so(n,\mathbb{R})$ consisting of skew-symmetric matrices, is $(n-2)tr(XY)$. Firstly, for $n=2$, that isn't even definite. Even when $n>2$, it isn't positive.  For any skew-symmetric matrix, its square is negative-semidefinite, which can be verified with any simple example. Thus, $(n-2)tr(X^2)\leq 0$ for skew-symmetric matrices. Am I going crazy?