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We describe two methods for computing p -modular Brauer character tables for groups of Lie type G (p f) in defining characteristic p , assuming that the ordinary character table of G (p f) is known, and the weight multiplicities of the corresponding algebraic group G are known for p -restricted highest weights. [ABSTRACT FROM AUTHOR]

Abstract: This paper is a contribution to the general program introduced by Isaacs, Malle and Navarro to prove the McKay conjecture in the representation theory of finite groups. We develop new methods for dealing with simple groups of Lie type in the defining characteristic case. Using a general argument based on the representation theory of connected reductive groups with disconnected center, we show that the inductive McKay condition holds if the Schur multiplier of the simple group has order 2. As a consequence, the simple groups and are “good” for and the simple groups are “good” for in the sense of Isaacs, Malle and Navarro. We also describe the action of the diagonal and field automorphisms on the semisimple and the regular characters. [Copyright &y& Elsevier]

Abstract: In this paper, we verify Dade''s invariant conjecture for Steinberg''s triality groups in the defining characteristic, i.e., in characteristic 2. Together with the results in [J. An, Dade''s conjecture for Steinberg triality groups 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 in the defining characteristic, i.e., is good for the prime 2 in the sense of Isaacs, Malle and Navarro. [Copyright &y& Elsevier]

Abstract: We verify Uno''s invariant conjecture for Steinberg''s triality groups , 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. [Copyright &y& Elsevier]