Diagram calculus for an affine $C$ Temperley--Lieb algebra, I

Details Diagram calculus for an affine $C$ Temperley--Lieb algebra, I Diagram calculus for an affine $C$ Temperley--Lieb algebra, I

2009-10-06

arxiv.org/abs/0910.0925v2

Mathematics

Quantum Algebra

35 pages, 104 figures minor typos fixed, wording improved in a few places, filenames for figures were renamed, Lemma 6.4.1 in

Scientific paper

In this paper, we present an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements (in the sense of Stembridge) of the Coxeter group of type affine $C$. Moreover, we provide an explicit description of a basis for the diagram algebra. In the sequel to this paper, we show that this diagrammatic representation is faithful. The results of this paper and its sequel will be used to construct a Jones-type trace on the Hecke algebra of type affine $C$, allowing us to non-recursively compute leading coefficients of certain Kazhdan--Lusztig polynomials.

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