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

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 $S_{N-1}$ to $S_N$.

25 pages, 2 figures

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