Invariant theory for coincidental complex reflection groups

  title={Invariant theory for coincidental complex reflection groups},
  author={Victor Reiner and Anne V. Shepler and Eric N. Sommers},
  journal={Mathematische Zeitschrift},
V.F. Molchanov considered the Hilbert series for the space of invariant skew-symmetric tensors and dual tensors with polynomial coefficients under the action of a real reflection group, and he speculated that it had a certain product formula involving the exponents of the group. We show that Molchanov’s speculation is false in general but holds for all coincidental complex reflection groups when appropriately modified using exponents and co-exponents. These are the irreducible well-generated (i… 
Eulerian representations for real reflection groups
  • Sarah Brauner
  • Mathematics
    Journal of the London Mathematical Society
  • 2022
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