Erratum for Fulton and Harris - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T00:49:09Z http://mathoverflow.net/feeds/question/108886 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108886/erratum-for-fulton-and-harris Erratum for Fulton and Harris Ben Lim 2012-10-05T03:20:33Z 2012-10-06T00:10:02Z <p>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. </p> <p>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?</p> <p>Thanks.</p> <p>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 $W_2$.</p> <p><strong>Edit:</strong> In case this question gets closed, you may notify me of any errors by email: u5034323@anu.edu.au </p> http://mathoverflow.net/questions/108886/erratum-for-fulton-and-harris/108908#108908 Answer by Jim Humphreys for Erratum for Fulton and Harris Jim Humphreys 2012-10-05T12:14:15Z 2012-10-05T12:14:15Z <p>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. </p> <p>All of us who consult the book of Fulton &amp; 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: <code>$a+b+1$</code> should be <code>$a+b+2$</code>.</p> <p>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 &amp; Harris is a first printing, so I'm unsure what if anything has been changed in later printings.) </p> http://mathoverflow.net/questions/108886/erratum-for-fulton-and-harris/108909#108909 Answer by Julien Puydt for Erratum for Fulton and Harris Julien Puydt 2012-10-05T12:19:09Z 2012-10-05T12:19:09Z <p>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!</p> <p>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).</p> <p>And it can be done likewise for other reference works.</p> http://mathoverflow.net/questions/108886/erratum-for-fulton-and-harris/108924#108924 Answer by hoxide for Erratum for Fulton and Harris hoxide 2012-10-05T15:04:52Z 2012-10-05T15:04:52Z <p>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 activate research area recently. While this mistake may cause confusions to non-expert.</p>