## Abstract

Let r,n be positive integers. Let e be 0 or an integer bigger than 1. Let v_{1},...,v_{r}∈Z/eZ and K_{r}(n) be the set of Kleshchev r-partitions of n with respect to (e;Q), where Q:=(v_{1},...,v_{r}). The Dipper-James-Murphy conjecture asserts that K_{r}(n) is the same as the set of (Q,e)-restricted bipartitions of n if r=2. In this paper we consider an extension of this conjecture to the case where r>2. We prove that any multi-core Λ=(Λ^{(1)},...,Λ^{(r)}) in K_{r}(n) is a (Q,e)-restricted r-partition. As a consequence, we show that in the case e=0, K_{r}(n) coincides with the set of (Q,e)-restricted r-partitions of n and also coincides with the set of ladder r-partitions of n.

Original language | English |
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Pages (from-to) | 78-93 |

Number of pages | 16 |

Journal | Journal of Combinatorial Theory. Series A |

Volume | 118 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2011 |

## Keywords

- Crystal basis
- Fock spaces
- Kleshchev multipartitions
- Ladder multipartitions
- Ladder nodes
- Lakshimibai-Seshadri paths