### Abstract

In this paper we prove two conjectures on partitions with certain conditions. A motivation for this is given by a problem in the modular representation theory of the covering groups Sn of the finite symmetric groups Sn in characteristic 5. One of the conjectures (Conjecture B below) has been open since 1974, when it was stated by the first author in his memoir [A3]. Recently the second and third author (jointly with A. O. Morris) arrived at essentially the same conjecture from a completely different direction. Their paper [BMO] was concerned with decomposition matrices of Sn in characteristic 3. A basic difficulty for obtaining similar results in characteristic 5 (or larger) was the lack of a class of partitions which would be "natural" character labels for the modular characters of these groups. In this connection two conjectures were stated (Conjectures A and B below), whose solutions would be helpful in the characteristic 5 case. One of them, Conjecture B, is equivalent to the old Conjecture B mentioned above. Conjecture A is concerned with a possible inductive definition of the set of partitions which should serve as the required labels.

Original language | English (US) |
---|---|

Pages (from-to) | 597-615 |

Number of pages | 19 |

Journal | Transactions of the American Mathematical Society |

Volume | 344 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1994 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*344*(2), 597-615. https://doi.org/10.1090/S0002-9947-1994-1220904-1

}

*Transactions of the American Mathematical Society*, vol. 344, no. 2, pp. 597-615. https://doi.org/10.1090/S0002-9947-1994-1220904-1

**Partition identities and labels for some modular characters.** / Andrews, George E.; Bessenrodt, C.; Olsson, J. B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Partition identities and labels for some modular characters

AU - Andrews, George E.

AU - Bessenrodt, C.

AU - Olsson, J. B.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - In this paper we prove two conjectures on partitions with certain conditions. A motivation for this is given by a problem in the modular representation theory of the covering groups Sn of the finite symmetric groups Sn in characteristic 5. One of the conjectures (Conjecture B below) has been open since 1974, when it was stated by the first author in his memoir [A3]. Recently the second and third author (jointly with A. O. Morris) arrived at essentially the same conjecture from a completely different direction. Their paper [BMO] was concerned with decomposition matrices of Sn in characteristic 3. A basic difficulty for obtaining similar results in characteristic 5 (or larger) was the lack of a class of partitions which would be "natural" character labels for the modular characters of these groups. In this connection two conjectures were stated (Conjectures A and B below), whose solutions would be helpful in the characteristic 5 case. One of them, Conjecture B, is equivalent to the old Conjecture B mentioned above. Conjecture A is concerned with a possible inductive definition of the set of partitions which should serve as the required labels.

AB - In this paper we prove two conjectures on partitions with certain conditions. A motivation for this is given by a problem in the modular representation theory of the covering groups Sn of the finite symmetric groups Sn in characteristic 5. One of the conjectures (Conjecture B below) has been open since 1974, when it was stated by the first author in his memoir [A3]. Recently the second and third author (jointly with A. O. Morris) arrived at essentially the same conjecture from a completely different direction. Their paper [BMO] was concerned with decomposition matrices of Sn in characteristic 3. A basic difficulty for obtaining similar results in characteristic 5 (or larger) was the lack of a class of partitions which would be "natural" character labels for the modular characters of these groups. In this connection two conjectures were stated (Conjectures A and B below), whose solutions would be helpful in the characteristic 5 case. One of them, Conjecture B, is equivalent to the old Conjecture B mentioned above. Conjecture A is concerned with a possible inductive definition of the set of partitions which should serve as the required labels.

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U2 - 10.1090/S0002-9947-1994-1220904-1

DO - 10.1090/S0002-9947-1994-1220904-1

M3 - Article

VL - 344

SP - 597

EP - 615

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -