The degree of the Hilbert-Poincar\'e polynomial of PBW-graded modules
  In this note, we study the Hilbert-Poincar\'e polynomials for the PBW-graded of simple modules for a simple complex Lie algebra. The computation of their degree can be reduced to modules of fundamental highest weight. We provide these degrees explicitly. 
Teodor Backhaus and Lara Bossinger and Christian Desczyk and Ghislain   Fourier
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