Diagram calculus for a type affine $C$ Temperley--Lieb algebra, II
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2011
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| _version_ | 1866917585200611328 |
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| author | Ernst, Dana C. |
| author_facet | Ernst, Dana C. |
| contents | In a previous paper, we presented 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 of the Coxeter group of type affine $C$. We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the so-called monomial basis of the Temperley--Lieb algebra of type affine $C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1101_4215 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Diagram calculus for a type affine $C$ Temperley--Lieb algebra, II Ernst, Dana C. Quantum Algebra 20F55, 20C08, 57M15 In a previous paper, we presented 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 of the Coxeter group of type affine $C$. We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the so-called monomial basis of the Temperley--Lieb algebra of type affine $C$. |
| title | Diagram calculus for a type affine $C$ Temperley--Lieb algebra, II |
| topic | Quantum Algebra 20F55, 20C08, 57M15 |
| url | https://arxiv.org/abs/1101.4215 |