Positive Jantzen sum formulas for cyclotomic Hecke algebras

@article{Mathas2022PositiveJS,
  title={Positive Jantzen sum formulas for cyclotomic Hecke algebras},
  author={Andrew Mathas},
  journal={Mathematische Zeitschrift},
  year={2022},
  volume={301},
  pages={2617 - 2658}
}
  • A. Mathas
  • Published 29 June 2021
  • Mathematics
  • Mathematische Zeitschrift
This paper proves a “positive” Jantzen sum formula for the Specht modules of the cyclotomic Hecke algebras of type A and uses it to obtain new bounds on decomposition numbers. Quite remarkably, our results are proved entirely inside the cyclotomic Hecke algebras. Our positive sum formula shows that, in the Grothendieck group, the Jantzen sum formula can be written as an explicit non-negative linear combination of modules [Ef,eν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage… 

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