## Abstract

In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S_{2} _{n}, B_{n}). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).

Original language | English |
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Pages (from-to) | 1111-1152 |

Number of pages | 42 |

Journal | Journal of Algebraic Combinatorics |

Volume | 45 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jun 1 2017 |

## Keywords

- Center of the hyperoctahedral group algebra
- Centers of group algebras
- Double-class algebras
- Hecke algebra of the pair(S × S , diag(S))
- Polynomiality property of the structure coefficients
- Structure coefficients

## ASJC Scopus subject areas

- Algebra and Number Theory
- Discrete Mathematics and Combinatorics