1. Introduction 2. Representation theory and $\psi ̂2$ in $K$-theory 3. Nice form for $\psi ̂2$ in $PK̂1(E_8)_{(5)}$ and $PK̂1(X)$ 4. Determination of $\upsilon ̂{-1}_1 \pi _{2m}(E_8; 5)$ 5. Determination of $\upsilon ̂{-1}_1 \pi _{2m-1}(E_8; 5)$ 6. Calculation of $\upsilon ̂{-1}_1\pi _*(E_8; 3)$ 7. LiE program for computing $\lambda ̂2$ in $R(E_8)$ 8. Analysis of $F_4$ and $E_7$ at the prime 3
Summary
Introduction Representation theory and $\psî2$ in $K$-theory Nice form for $\psî2$ in $PK̂1(E_8)_{(5)}$ and $PK̂1(X)$ Determination of $v_1̂{-1}\pi_{2m}(E_8;5)$ Determination of $v_1̂{-1}\pi_{2m-1}(E_8;5)$ Calculation of $v_1̂{-1}\pi_\ast(E_8;3)$ LiE program for computing $\lambdâ2$ in $R(E_8)$ Analysis of $F_4$ and $E_7$ at the prime $3$ References
