Geodesic
Combinatorics of centers of 0-Hecke algebras in type \(A\)
Sebastian König1
1Institute of Algebra, Number Theory and Discrete Mathematics, Leibniz University Hannover
The electronic journal of combinatorics, Tome 30 (2023) no. 3
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A basis of the center of the 0-Hecke algebra of an arbitrary finite Coxeter group was described by He in 2015. This basis corresponds to certain equivalence classes of the Coxeter group. We consider case of the symmetric group $S_n$. Building on work of Geck, Kim and Pfeiffer, we obtain a complete set of representatives of the equivalence classes. This set is naturally parametrized by certain compositions of $n$ called maximal. We develop an explicit combinatorial description for the equivalence classes that are parametrized by the maximal compositions whose odd parts form a hook.
DOI : 10.37236/11126
Classification : 20F55, 05E16, 20B30, 20C08
Mots-clés : Coxeter group, symmetric group, hook, Hecke algebra

Sebastian König  1

1 Institute of Algebra, Number Theory and Discrete Mathematics, Leibniz University Hannover 
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     title = {Combinatorics of centers of {0-Hecke} algebras in type {\(A\)}},
     journal = {The electronic journal of combinatorics},
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Sebastian König. Combinatorics of centers of 0-Hecke algebras in type \(A\). The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11126

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