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arXiv · 1608.04055

An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications

Weideng Cui
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Abstract

Inspired by the work [PA], we establish an explicit algebra isomorphism between the degenerate cyclotomic Yokonuma-Hecke algebra $Y_{r,n}^{d}(q)$ and a direct sum of matrix algebras over tensor products of degenerate cyclotomic Hecke algebras of type $A$. We then develop several applications of this result, including a new proof of the modular representation theory of $Y_{r,n}^{d}(q)$, a semisimplicity criterion for it and cellularity of it. Moreover, we prove that $Y_{r,n}^{d}(q)$ is a symmetric algebra and determine the associated Schur elements by using the isomorphism theorem for it.

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Weideng Cui. 2016-08-14. An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications. https://arxiv.org/abs/1608.04055

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