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A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of $S_N$
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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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 $H_0(S_N)$. 
@article{DMTCS_2010_special_259_a16,
     author = {Denton, Tom},
     title = {A {Combinatorial} {Formula} for {Orthogonal} {Idempotents} in the $0${-Hecke} {Algebra} of $S_N$},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)},
     year = {2010},
     doi = {10.46298/dmtcs.2821},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2821/}
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Denton, Tom. A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of $S_N$. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2821. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2821/

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