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.
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2000 Mathematics Subject Classification:
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.