Idempotents of the Hecke algebra become Schur functions in the skein of the annulus

The Hecke algebra H_n contains well known idempotents E_{lambda} which are indexed by Young diagrams with n cells. They were originally described by Gyoja. A skein theoretical description of E_{lambda} was given by Aiston and Morton. The closure of E_{lambda} becomes an element Q_{lambda} of the skein of the annulus. In this skein, they are known to obey the same multiplication rule as the symmetric Schur functions s_{lambda}. But previous proofs of this fact used results about quantum groups which were far beyond the scope of skein theory. Our elementary proof uses only skein theory and basic algebra.