Erratum for Fulton and Harris

Being somewhat error-prone myself, I'm well aware of the need to collect errata in some systematic way. In the Internet age this has often been done in ad hoc ways on individual homepages, though some publishers (like AMS) are trying to establish durable book pages at their site with updates and errata posted by the authors from time to time.

All of us who consult the book of Fulton & Harris tend to view some of the passages as written down too informally, but there are also some outright errors. For example, many people seem to have trouble following the proof of Proposition 15.15, while Exercise 15.19 has an obvious error in the special case of Weyl's dimension formula: $a+b+1$ should be $a+b+2$.

I did try (unsuccessfully) at one point to get direct clarification from the authors, but it would be optimal for Springer to coordinate the collection of errata. Printing technology now favors print-on-demand and e-books, but these are cheapest when no changes are made in the original printing plates made from a TeX file. Even though it's easy to correct a TeX file, that by itself doesn't motivate publishers to issue corrected reprints. So they do have a responsibility to provide more help to readers in other ways. (By the way, my copy of Fulton & Harris is a first printing, so I'm unsure what if anything has been changed in later printings.)

My answer is similar to that of J.Humphreys in that I think there should be a central place for errata ; but I have a more audacious proposition : use the book's wikipedia page!

That way, we don't need the publisher to do something, and we're able to do something by ourselves (where "we" is the mathematical community).

And it can be done likewise for other reference works.

I think there may be a "serious" mistake in the section of branching rules: equation (25.37) and (25.39) on Page 427 (GTM 129, 1991). The formulas actually only true for the "stable case", which is $\lambda_i = 0$ when $i>\lfloor m/2\rfloor$ in case $(O_{m}\mathbb{C},GL_{m}\mathbb{C})$; $\lambda_i = 0$ when $i>n$ in case $(Sp_{2n}\mathbb{C}, GL_{2n}\mathbb{C})$. One may read "Roger Howe, Eng-Chye Tan, Willenbring, Stable Branching Rules for Classical Symmetric Pairs" for a conceptually simpler proof of this formula. However, a "clean" (or rather "useful") branching formulas for non-stable case are still unknown currently (up to my understanding). I think finding such formula is still an active research area recently, while this mistake may cause confusions to non-expert.