The quasiharmonic deformation conjecture for singular vectors
The quasiharmonic deformation conjecture for singular vectors
Let be a real reflection group with reflection representation , let be the universal rational Cherednik algebra, and let be the space of universal quasiharmonics. For a parameter , write for the polynomial representation, call a vector singular if it is annihilated by all Dunkl operators, and write for the specialization at . Quasiharmonic deformation conjecture. For every singular function , all the singular vectors of belong to
Equivalently, the space of singular vectors in should be deformable within the class of quasiharmonics. The conjecture is proved for dihedral groups in the cases described by the source, while computations for symmetric groups support it; the general statement remains open.
Sources & referencesView supporting material
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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