Dade's Invariant Conjecture for the Symplectic Group Sp₄(2ⁿ) and the Special Unitary Group SU₄(2²ⁿ) in Defining Characteristic

Abstract

In this article, we verify Dade's projective invariant conjecture for the symplectic group Sp₄(2 ⁿ ) and the special unitary group SU₄(2²ⁿ ) in the defining characteristic, that is, in characteristic 2. Furthermore, we show that the Isaacs–Malle–Navarro version of the McKay conjecture holds for Sp₄(2 ⁿ ) and SU₄(2²ⁿ ) in the defining characteristic, that is, Sp₄(2 ⁿ ) and SU₄(2²ⁿ ) are good for the prime 2 in the sense of Isaacs, Malle, and Navarro.

Key Words:

• Dade's conjecture
• McKay'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 during a visit of the second author at the Department of Mathematics of the University of Auckland. He wishes to express his sincere thanks to all the persons of the department for their hospitality. Part of this work was done while the third author visited Chiba University in Japan. He would like to thank Professor Shigeo Koshitani for his support and great hospitality, and also to the Japan Society for the Promotion of Science (JSPS) for supporting his research.

Notes

Communicated by D. Nakano.