Idempotents of the Hecke algebra become Schur functions in the skein of the annulus
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:math/0110119
 Bibcode:
 2001math.....10119L
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Quantum Algebra;
 57M25
 EPrint:
 17 pages, 11 figures