### Abstract

Dedicated to Peter M. Neumann on the occasion of his seventieth birthday We develop cycle index generating functions for orthogonal groups in even characteristic and give some enumerative applications. A key step is the determination of the values of the complex linear-Weil characters of the finite symplectic group, and their induction to the general linear group, at unipotent elements. We also define and study several natural probability measures on integer partitions.

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

Pages (from-to) | 2539-2566 |

Number of pages | 28 |

Journal | Transactions of the American Mathematical Society |

Volume | 364 |

Issue number | 5 |

DOIs | |

State | Published - 2012 |

### Fingerprint

### Keywords

- Cycle index
- Random matrix
- Random partition
- Weil representation

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*364*(5), 2539-2566. https://doi.org/10.1090/S0002-9947-2012-05406-7

**Cycle indices for finite orthogonal groups of even characteristic.** / Fulman, Jason; Saxl, Jan; Tiep, Pham Huu.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 364, no. 5, pp. 2539-2566. https://doi.org/10.1090/S0002-9947-2012-05406-7

}

TY - JOUR

T1 - Cycle indices for finite orthogonal groups of even characteristic

AU - Fulman, Jason

AU - Saxl, Jan

AU - Tiep, Pham Huu

PY - 2012

Y1 - 2012

N2 - Dedicated to Peter M. Neumann on the occasion of his seventieth birthday We develop cycle index generating functions for orthogonal groups in even characteristic and give some enumerative applications. A key step is the determination of the values of the complex linear-Weil characters of the finite symplectic group, and their induction to the general linear group, at unipotent elements. We also define and study several natural probability measures on integer partitions.

AB - Dedicated to Peter M. Neumann on the occasion of his seventieth birthday We develop cycle index generating functions for orthogonal groups in even characteristic and give some enumerative applications. A key step is the determination of the values of the complex linear-Weil characters of the finite symplectic group, and their induction to the general linear group, at unipotent elements. We also define and study several natural probability measures on integer partitions.

KW - Cycle index

KW - Random matrix

KW - Random partition

KW - Weil representation

UR - http://www.scopus.com/inward/record.url?scp=84856683984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856683984&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2012-05406-7

DO - 10.1090/S0002-9947-2012-05406-7

M3 - Article

AN - SCOPUS:84856683984

VL - 364

SP - 2539

EP - 2566

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -