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

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

2001-10-11

arxiv.org/abs/math/0110119v1

Math. Proc. Camb. Phil. Soc 138 (2005), 79-96

Mathematics

Geometric Topology

17 pages, 11 figures

Scientific paper

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.

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