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PreprintCC BY 4.0arXiv

The Harish-Chandra isomorphism for supersymmetric spaces and ghost distributions

  • Shifra Reif
  • Siddhartha Sahi
  • Vera Serganova
  • Alexander Sherman
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Abstract

We prove the Harish-Chandra isomorphism theorem for supersymmetric spaces, describing the polynomial algebra of eigenvalues of invariant differential operators. The polynomials obtained satisfy novel invariance conditions, which remain somewhat mysterious. We also prove the Harish-Chandra isomorphism for ghost distributions, which satisfy a `square root' of the invariance conditions coming from invariant differential operators. All proofs are algebraic, and rely on a rank-one reduction argument and the Chevalley restriction theorem.

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Cite

BibTeXRIS
BibTeX
@misc{reif2026harishchandra,
  title = {{The Harish-Chandra isomorphism for supersymmetric spaces and ghost distributions}},
  author = {Shifra Reif and Siddhartha Sahi and Vera Serganova and Alexander Sherman},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2606.11407},
  eprint = {2606.11407},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.11407},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Harish-Chandra isomorphism for supersymmetric spaces and ghost distributions
AU  - Shifra Reif
AU  - Siddhartha Sahi
AU  - Vera Serganova
AU  - Alexander Sherman
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2606.11407
UR  - https://arxiv.org/abs/2606.11407
AB  - We prove the Harish-Chandra isomorphism theorem for supersymmetric spaces, describing the polynomial algebra of eigenvalues of invariant differential operators. The polynomials obtained satisfy novel invariance conditions, which remain somewhat mysterious. We also prove the Harish-Chandra isomorphism for ghost distributions, which satisfy a `square root' of the invariance conditions coming from invariant differential operators. All proofs are algebraic, and rely on a rank-one reduction argument and the Chevalley restriction theorem.
ER  -