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- W2949154692 abstract "We give a presentation of the endomorphism algebra $End_{cU_q(fsl_2)}(V^{otimes r})$, where $V$ is the 3-dimensional irreducible module for quantum $fsl_2$ over the function field $C(q^{{1/2}})$. This will be as a quotient of the Birman-Wenzl-Murakami algebra $BMW_r(q):=BMW_r(q^{-4},q^2-q^{-2})$ by an ideal generated by a single idempotent $Phi_q$. Our presentation is in analogy with the case where $V$ is replaced by the 2- dimensional irreducible $cU_q(fsl_2)$-module, the BMW algebra is replaced by the Hecke algebra $H_r(q)$ of type $A_{r-1}$, $Phi_q$ is replaced by the quantum alternator in $H_3(q)$, and the endomorphism algebra is the classical realisation of the Temperley-Lieb algebra on tensor space. In particular, we show that all relations among the endomorphisms defined by the $R$-matrices on $V^{otimes r}$ are consequences of relations among the three $R$-matrices acting on $V^{otimes 4}$. The proof makes extensive use of the theory of cellular algebras. Potential applications include the decomposition of tensor powers when $q$ is a root of unity." @default.
- W2949154692 created "2019-06-27" @default.
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- W2949154692 date "2008-06-24" @default.
- W2949154692 modified "2023-09-27" @default.
- W2949154692 title "On endomorphisms of quantum tensor space" @default.
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