4 N ov 1 99 8 ON REPRESENTATIONS OF AFFINE TEMPERLEY – LIEB ALGEBRAS , II
نویسندگان
چکیده
We study some non-semisimple representations of affine Temperley–Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite dimensional cellular algebra.
منابع مشابه
Commuting families in Hecke and Temperley-Lieb Algebras
We define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements i...
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Construction of the diagrammatic version of the affine Temperley-Lieb algebra of type A N as a subring of matrices over the Laurent polynomials is given. We move towards geometrical understanding of cellular structure of the Temperley-Lieb algebra. We represent its center as a coordinate ring of the certain affine algebraic variety and describe this variety constructing its desingularization.
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