## Abstract

The Hecke algebra of the pair (S_{2n}, B_{n}), where B_{n} is the hyperoctahedral subgroup of 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 (S_{2n}, B_{n}) for every n. To build it, by using partial bijections we introduce and study a new class of finite dimensional algebras.

Original language | English |
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Article number | P4.35 |

Journal | Electronic Journal of Combinatorics |

Volume | 21 |

Issue number | 4 |

Publication status | Published - Nov 13 2014 |

Externally published | Yes |

## Keywords

- Hecke algebra of (S, B)
- Partial bijections
- Structure coefficients

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

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