Idempotents of the Hecke algebra become Schur functions in the skein of the annulus
Sascha G. Lukac
Abstract
The Hecke algebra Hn contains well known idempotents Eλ which are indexed by Young diagrams with n cells. They were originally described by Gyoja. A skein theoretical description of Eλ was given by Aiston and Morton. The closure of Eλ becomes an element Qλ of the skein of the annulus. In this skein, they are known to obey the same multiplication rule as the symmetric Schur functions sλ. 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.
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