Generalised Temperley-Lieb algebras of type $G(r,1,n)$

preprint2022arXivOpen access

In this paper, we define a quotient of the cyclotomic Hecke algebra of type $G(r,1,n)$ as a generalisation of the Temperley-Lieb algebras of type $A$ and $B$ . We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of $KLR$ algebras, determine the corresponding decomposition matrix.

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Generalised Temperley-Lieb algebras of type $G(r,1,n)$

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Generalised Temperley-Lieb algebras of type G(r,1,n)G(r,1,n)G(r,1,n)

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Generalised Temperley-Lieb algebras of type $G(r,1,n)$