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For notation and general facts about Lie algebras see Carter(1972) or Humphreys (1972). ... In order to determine the sign we follow the method of Carter(1972), 4.2.
www.maths.usyd.edu.au/u/bobh/hrt.pdf
Mathas, Carter-Payne homomorphisms and Jantzen filtrations, J. Algebraic Combin., 32. (2010), 417–457. ... Mathas, Cyclotomic Carter-Payne homomorphisms, Represent. Theory, 18 (2014),. Andrew Mathas July 2024.
www.maths.usyd.edu.au/u/mathas/MathasCV.pdf