On the canonical GL_2~(F_2)-module structure of K(n)~*(BZ/2 * BZ/2)

摘要

Let K(n)~*(-) be the n-th Morava K-theory at 2. We discuss the existence in K(n)~* (BZ/2 * BZ/2) of a basis whose elements are just permuted by the canonical action of GL_2 (F_2) approx= Aut (Z/2 * Z/2). We exhibit such a basis when n = 3 and prove that it does not exist when n = 2.