λ-rings: Definitions and basic propertiesbeta version, not proofread! UPDATE: This project has found a new home at https://github.com/darijgr/lambda .The files below might be out of date.
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 A@B.com with A = darijgrinberg and B = gmail |