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

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.

arXiv commenta work inspired by others'. We point out the fact that the isomorphism can also be deduced from the results in [Ro]

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• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Schur elements for the Ariki-Koike algebra and applications
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Cited by in corpus (1)

• Affine wreath product algebras