Abstract
We show that, over an arbitrary field, q-rook monoid algebras are iterated inflations of Iwahori-Hecke algebras, and, in particular, are cellular. Furthermore we give an algebra decomposition which shows a q-rook monoid algebra is Morita equivalent to a direct sum of Iwahori-Hecke algebras. We state some of the consequences for the representation theory of q-rook monoid algebras.
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Paget, R. Representation theory of q-rook monoid algebras. J Algebr Comb 24, 239–252 (2006). https://doi.org/10.1007/s10801-006-0010-y
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DOI: https://doi.org/10.1007/s10801-006-0010-y