### Abstract

The 0-Hecke algebra H _{n} (0) is a deformation of the group algebra of the symmetric group Sn. We show that its coinvariant algebra naturally carries the regular representation of H _{n} (0), giving an analogue of the well-known result for Sn by Chevalley-Shephard-Todd. By investigating the action of H _{n} (0) on coinvariants and flag varieties, we interpret the generating functions counting the permutations with fixed inverse descent set by their inversion number and major index. We also study the action of H _{n} (0) on the cohomology rings of the Springer fibers, and similarly interpret the (non-commutative) Hall-Littlewood symmetric functions indexed by hook shapes.

Original language | English (US) |
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Pages (from-to) | 245-278 |

Number of pages | 34 |

Journal | Journal of Algebraic Combinatorics |

Volume | 40 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 2014 |

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### Keywords

- 0-Hecke algebra
- Coinvariant algebra
- Demazure operator
- Descent monomial
- Flag variety
- Hall-Littlewood function
- Ribbon number
- Springer fiber

### ASJC Scopus subject areas

- Algebra and Number Theory
- Discrete Mathematics and Combinatorics