The W-goodness finite-dimensional quotient conjecture
Let be a real reflection group with reflection representation . A positive integer is -good if, for every parameter with , the Cherednik algebra admits a finite-dimensional module of the form , where is an irreducible -submodule of dimension . Let be the distinguished copy of the defining module in the degree- quasiharmonics at parameter . W-goodness quotient conjecture. If is -good, then
is finite-dimensional. The conjecture connects the universal quasiharmonic submodule with the finite-dimensional representations guaranteed by -goodness. The source provides examples of -good integers for types , , , and , but does not establish the conjecture in general.
References
Primary source
Arkady Berenstein and Yurii Burman, “Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras”, arXiv:math/0505173 (2007).
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