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

Sascha G. Lukac

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arXiv · math/0110119

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

Sascha G. Lukac

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Abstract

The Hecke algebra H_n contains well known idempotents E_λ which are indexed by Young diagrams with n cells. They were originally described by Gyoja. A skein theoretical description of E_λ was given by Aiston and Morton. The closure of E_λ becomes an element Q_λ of the skein of the annulus. In this skein, they are known to obey the same multiplication rule as the symmetric Schur functions s_λ. 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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BibTeX RIS

Sascha G. Lukac. 2001-10-11. Idempotents of the Hecke algebra become Schur functions in the skein of the annulus. https://arxiv.org/abs/math/0110119

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