On Tensor Spaces for Rook Monoid Algebras

2014/11/22 by Xiao, Zhankui
#05E10 #20G05 #20M30 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1411.6120

Abstract

Let m,n∈ ℕ, and V be a m-dimensional vector space over a field F of characteristic 0. Let U=F⊕ V and R_n be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U^{⊗ 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^{⊗ n} in FR_n.

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