Work

Loop spaces, twistor $\mathbb P^1$ and tempiric parameters

Year: 2026

Type: preprint

Abstract: We establish bijections among spherical orbits on loop symmetric spaces, principal bundles on the twistor $\mathbb P^1$, and tempiric Langlands parameters. Using Vogan's theory of minimal $K$-types, we further establish bijections among irreducible equivariant local systems on loop symmetric spaces, irreducible local systems on principal bundles on the twistor $\mathbb P^1$, and irreducible representations of all strong inner forms of the dual symmetric subgroup. The latter bijections may be viewed as a combinatorial shadow of geometric Langlands duality for real reductive groups.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.16246

Authors: Chen, Tsao-Hsien, Yi, Lingfei

Institutions: University of Minnesota, Fudan University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Fudan University

Award: CAREER: Hitchin morphisms, relative Langlands duality, and automorphic L-functions

OpenAlex ID: W7213413473

Cites: 3

Cited by:

Related to: 10