λ-rings: Definitions and basic properties
beta version, not proofread! current version: 0.0.17, last revised 29 Dec 2012

This was written as accompanying material for an 1-hour talk I gave in a K-theory seminar. It has rapidly grown out of the 1-hour limits, though...

At the moment, this text mostly follows Donald Knutson, Lambda-Rings and the Representation Theory of the Symmetric Group, 1973. In future, I am planning to also include some results from William Fulton, Serge Lang, Riemann-Roch algebra, 1985 (altering them slightly in order to remove the positive structure constraints).

Topics covered as for now:
definitions of λ-rings and special lambda-rings;
examples (binomial λ-rings);
Grothendieck's Λ(K);
Adams operations (for special and non-special λ-rings; however the advanced facts are not being discussed);
Todd homomorphisms;
λ-verification principle (not in its strongest form, but in a form that works in most cases).

Please mail all typos/mistakes/annoyances you find in this text to me! My email address is with A = darijgrinberg and B = gmail
Darij Grinberg,
Apr 9, 2013, 11:59 PM
Darij Grinberg,
Apr 9, 2013, 11:59 PM