Dade's invariant conjecture for Steinberg's triality groups D43(2n) in defining characteristic

AbstractIn this paper, we verify Dade's invariant conjecture for Steinberg's triality groups D43(2n) in the defining characteristic, i.e., in characteristic 2. Together with the results in [J. An, Dade's conjecture for Steinberg triality groups D43(q) in non-defining characteristics, Math. Z. 241 (2002) 445–469] and [J. An, F. Himstedt, S. Huang, Uno's invariant conjecture for Steinberg's triality groups in defining characteristic, in preparation], this completes the proof of Dade's conjecture for Steinberg's triality groups. Furthermore, we show that the Isaacs–Malle–Navarro version of the McKay conjecture holds for D43(2n) in the defining characteristic, i.e., D43(2n) is good for the prime 2 in the sense of Isaacs, Malle and Navarro