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Unitary representations of the Cherednik algebra: \(V^*\)-homology

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Abstract

We give a non-negative combinatorial formula, in terms of Littlewood-Richardson numbers, for the \(V^*\)-homology of the unitary representations of the cyclotomic rational Cherednik algebra, and as a consequence, for the graded Betti numbers for the ideals of a class of subspace arrangements arising from the reflection arrangements of complex reflection groups.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA

    Susanna Fishel

  2. Instituto de Matemáticas, Universidad de Talca, Talca, Chile

    Stephen Griffeth & Elizabeth Manosalva

Authors
  1. Susanna Fishel
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  2. Stephen Griffeth
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  3. Elizabeth Manosalva
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Correspondence to Stephen Griffeth.

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We thank Bernard Leclerc and an anonymous referee for helpful comments. The second author acknowledges the financial support of Fondecyt Proyecto Regular 1190597. This work was supported by a grant from the Simons Foundation (#359602, Susanna Fishel)

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Fishel, S., Griffeth, S. & Manosalva, E. Unitary representations of the Cherednik algebra: \(V^*\)-homology. Math. Z. 299, 2215–2255 (2021). https://doi.org/10.1007/s00209-021-02746-2

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