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) |
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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 |
Externally published | Yes |
Keywords
- Cycle index
- Random matrix
- Random partition
- Weil representation
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics