Geodesic
Structure coefficients of the Hecke algebra of \((\mathcal{S}_{2n},\mathcal{B}_n)\)
Omar Tout1
1Université de Bordeaux
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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The Hecke algebra of the pair $(\mathcal{S}_{2n},\mathcal{B}_n)$, where $\mathcal{B}_n$ is the hyperoctahedral subgroup of $\mathcal{S}_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra. In this paper, we give a polynomiality property of its structure coefficients. Our main tool is a combinatorial algebra which projects onto the Hecke algebra of $(\mathcal{S}_{2n},\mathcal{B}_n)$ for every $n$. To build it, by using partial bijections we introduce and study a new class of finite dimensional algebras.
DOI : 10.37236/3592
Classification : 20C08
Mots-clés : Hecke algebra of \((\mathcal{S}_{2n},\mathcal{B}_n)\), partial bijections, structure coefficients

Omar Tout  1

1 Université de Bordeaux 
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     author = {Omar Tout},
     title = {Structure coefficients of the {Hecke} algebra of {\((\mathcal{S}_{2n},\mathcal{B}_n)\)}},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {4},
     doi = {10.37236/3592},
     zbl = {1302.05207},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3592/}
}
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Omar Tout. Structure coefficients of the Hecke algebra of \((\mathcal{S}_{2n},\mathcal{B}_n)\). The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/3592

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