Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chen, Tsao-Hsien, Yi, Lingfei
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7215091429