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Singularities of orbit closures in loop spaces of symmetric varieties II: twisted cases

  • Tsao-Hsien Chen
  • Lingfei Yi
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Abstract

We study the singularities of orbit closures in loop symmetric varieties, extending our previous work https://arxiv.org/abs/2310.20006 to the twisted setting. We prove that the IC complexes of orbit closures are pointwise pure and satisfy a parity-vanishing property. We apply these geometric results to the study of twisted affine Lusztig--Vogan modules, establishing foundational results, including positivity properties of the twisted affine Kazhdan--Lusztig--Vogan polynomials. Along the way, we construct conical symplectic transversal slices in loop symmetric spaces. We provide applications to Langlands duality for real groups.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026singularities,
  title = {{Singularities of orbit closures in loop spaces of symmetric varieties II: twisted cases}},
  author = {Tsao-Hsien Chen and Lingfei Yi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39079},
  eprint = {2609.39079},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39079},
}
RIS
TY  - UNPB
TI  - Singularities of orbit closures in loop spaces of symmetric varieties II: twisted cases
AU  - Tsao-Hsien Chen
AU  - Lingfei Yi
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39079
UR  - https://arxiv.org/abs/2609.39079
AB  - We study the singularities of orbit closures in loop symmetric varieties, extending our previous work https://arxiv.org/abs/2310.20006 to the twisted setting. We prove that the IC complexes of orbit closures are pointwise pure and satisfy a parity-vanishing property. We apply these geometric results to the study of twisted affine Lusztig--Vogan modules, establishing foundational results, including positivity properties of the twisted affine Kazhdan--Lusztig--Vogan polynomials. Along the way, we construct conical symplectic transversal slices in loop symmetric spaces. We provide applications to Langlands duality for real groups.
ER  -