@article{01JJD087XCFYPGNND2C80GE8XW,
  abstract     = {{For a finite dimensional representation Vof a finite reflection group W, we consider the rational Cherednik algebra H-t,H-c(V, W) associated with (V, W) at the parameters t not equal 0and c. The Dunkl total angular momentum algebra O-t,O-c(V, W) arises as the centraliser algebra of the Lie super-algebra osp(1|2) containing a Dunkl deformation of the Dirac operator, inside the tensor product of H-t,H-c(V, W) and the Clifford algebra generated by V.

 We show that when dim V >= 3 and for every value of the parameter c, the centre of O-t,O-c(V, W) is isomorphic to a univariate polynomial ring. Notably, the generator of the centre changes depending on whether or not (-1)(V) is an element of the group W. Using this description of the centre, and using the projection of the pseudo scalar from the Clifford algebra into O-t,O-c(V, W), we establish results analogous to "Vogan's conjecture" for a family of operators depending on suitable elements of the double cover (W) over tilde. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).}},
  author       = {{Calvert, Kieran and Gonçalves De Martino, Marcelo and Oste, Roy}},
  issn         = {{0021-8693}},
  journal      = {{JOURNAL OF ALGEBRA}},
  keywords     = {{DIRAC COHOMOLOGY,PROJECTIVE-REPRESENTATIONS,DUAL PAIR,OPERATORS,Dunkl operators,Dirac operators,Deformed Howe duality}},
  language     = {{eng}},
  pages        = {{198--226}},
  title        = {{The centre of the Dunkl total angular momentum algebra}},
  url          = {{http://doi.org/10.1016/j.jalgebra.2024.05.054}},
  volume       = {{658}},
  year         = {{2024}},
}

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