Year: 2026
Type: preprint
Abstract: We investigate the explicit geometric and combinatorial structure of Mirković-Vilonen (MV) cycles in twisted affine Grassmannians associated with special parahoric group schemes. Using the twist map on configuration spaces of decorated flags, we obtain an explicit parametrization of twisted MV cycles by Lusztig data. We show that the changes between reduced words are governed by the usual Lusztig transformations for the reductive group arising from ramified geometric Satake correspondence. As a consequence, the moment polytopes of twisted MV cycles coincide with the usual MV polytopes for this group. Our construction applies to all special parahoric subgroups in the tamely ramified setting.
Source: arXiv (Cornell University)
Authors: Hong, Jiuzu, Shen, Linhui, Weng, Daping
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220731980