Uno's Invariant Conjecture for the Finite Symplectic Group Sp₄(q) in the Defining Characteristic

Abstract

In this article, we verify Uno's invariant conjecture for the finite symplectic group Sp₄(q), q a power of an odd prime p, in the defining characteristic p. Uno's invariant conjecture is a refinement of Dade's invariant conjecture. Together with the results in [3], this completes the proof of Dade's invariant conjecture for the group Sp₄(q) in the defining characteristic.

Key Words:

• Dade's invariant conjecture
• Defining characteristic
• Symplectic groups
• Uno's conjecture

2000 Mathematics Subject Classification:

• Primary 20C20, 20C40

ACKNOWLEDGMENTS

The authors are very grateful to the Marsden Fund (of New Zealand) for financial support, via award number UOA 0721. Part of this work was done while the second author visited Chiba University in Japan. He would like to thank Professor Shigeo Koshitani for his support and great hospitality. He also acknowledges the support of a JSPS postdoctoral fellowship from the Japan Society for the Promotion of Science.

Notes

Communicated by D. Nakano.