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On Tensor Spaces for Rook Monoid Algebras (1411.6120v1)
Published 22 Nov 2014 in math.RA, math.GR, and math.RT
Abstract: Let $m,n\in \mathbb{N}$, and $V$ be a $m$-dimensional vector space over a field $F$ of characteristic $0$. Let $U=F\oplus V$ and $R_n$ be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of $U{\otimes n}$ in $FR_n$, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of $U{\otimes n}$ in $FR_n$.