On tensor spaces for rook monoid algebras |
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Authors: | Zhan Kui Xiao |
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Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P. R. China |
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Abstract: | Let m, n ∈ N, and V be an m-dimensional vector space over a field F of characteristic 0. Let U = F ⊕V and Rn be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of U⊗n in FRn, 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 FRn. |
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Keywords: | Rook monoid tensor space general linear group symmetric group |
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