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arXiv · 2512.10202

Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras

Jun Hu·Huansheng Li
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Abstract

In this paper we compute the explicit value of the standard symmetrizing form of the cyclotomic Hecke algebra of type $G(\ell,1,n)$ on each Murphy basis element. We do this for both the non-degenerate cyclotomic Hecke algebra of type $G(\ell,1,n)$ and the degenerate cyclotomic Hecke algebra of type $G(\ell,1,n)$. As an application, we obtain some equations on the coefficients which occur in the transition matrix between the Murphy basis elements and the seminormal basis elements of the cyclotomic Hecke algebra of type $G(\ell,1,n)$.

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Jun Hu, Huansheng Li. 2025-12-11. Standard symmetrizing forms and Murphy bases of the cyclotomic Hecke algebras. https://arxiv.org/abs/2512.10202

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