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A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of $S_N$

Abstract : Building on the work of P.N. Norton, we give combinatorial formulae for two maximal decompositions of the identity into orthogonal idempotents in the $0$-Hecke algebra of the symmetric group, $\mathbb{C}H_0(S_N)$. This construction is compatible with the branching from $H_0(S_{N-1})$ to $H_0(S_N)$.
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Tom Denton. A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of $S_N$. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.701-712. ⟨hal-01186249⟩

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