McKay matrices for finite-dimensional Hopf algebras

  title={McKay matrices for finite-dimensional Hopf algebras},
  author={Georgia Benkart and Rekha Biswal and Ellen E. Kirkman and Van C. Nguyen and Jieru Zhu},
  journal={Canadian Journal of Mathematics},
  pages={686 - 731}
Abstract For a finite-dimensional Hopf algebra $\mathsf {A}$ , the McKay matrix $\mathsf {M}_{\mathsf {V}}$ of an $\mathsf {A}$ -module $\mathsf {V}$ encodes the relations for tensoring the simple $\mathsf {A}$ -modules with $\mathsf {V}$ . We prove results about the eigenvalues and the right and left (generalized) eigenvectors of $\mathsf {M}_{\mathsf {V}}$ by relating them to characters. We show how the projective McKay matrix $\mathsf {Q}_{\mathsf {V}}$ obtained by tensoring… 

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