### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 2467-2488 |

Number of pages | 22 |

Journal | Journal of Pure and Applied Algebra |

Volume | 216 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Diagram calculus for a type affine C Temperley-Lieb algebra, I.** / Ernst, Dana C.

Research output: Contribution to journal › Article

*Journal of Pure and Applied Algebra*, vol. 216, no. 11, pp. 2467-2488. https://doi.org/10.1016/j.jpaa.2012.03.013

}

TY - JOUR

T1 - Diagram calculus for a type affine C Temperley-Lieb algebra, I

AU - Ernst, Dana C

PY - 2012/11

Y1 - 2012/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84861835503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861835503&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2012.03.013

DO - 10.1016/j.jpaa.2012.03.013

M3 - Article

VL - 216

SP - 2467

EP - 2488

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 11

ER -