In my book Elliptic operators, topology and asymptotic methods (both the first and the second editions) I give a discussion of the representation theory of the groups Spin and Pin which was based (as far as I can now remember) on some notes that I took when I attended Adams’ famous course on the exceptional Lie groups, as a Part III student in 1981.  I no longer seem to have those, unfortunately (although meanwhile a version of Adams’ own notes on his approach has been published by University of Chicago Press).  Meanwhile, in 2010 Darij Grinberg pointed out on Math Overflow that the argument I gave was garbled: see this link.  In this post I want to explain what is garbled and how the useful part of the argument can be recovered.  Continue reading →