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- W2952176875 abstract "We study the combinatorial representation theory of the ``planar rook $P_n$. This algebra has a basis consisting of planar rook diagrams and multiplication given by diagram concatenation. For each integer $0 le k le n$, we construct natural representations $V^n_k$ which form a complete set of non-isomorphic, irreducible $P_n$-representations. We explicitly decompose the regular representation of $P_n$ into a direct sum of irreducible modules. We compute the Bratteli diagram for the tower of algebras $P_0 subseteq P_1 subseteq P_2 subseteq ...$ and show that this Bratteli diagram is Pascal's triangle. In fact, we show that many of the binomial identities, both additive and multiplicative, have interpretations in terms of the representation theory of the planar rook algebra." @default.
- W2952176875 created "2019-06-27" @default.
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- W2952176875 date "2008-06-24" @default.
- W2952176875 modified "2023-09-26" @default.
- W2952176875 title "The Planar Rook Algebra and Pascal's Triangle" @default.
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