Howe duality and dichotomy for exceptional theta correspondences

• 成果类型: Article
• 署名作者: Gan, Wee Teck; Savin, Gordan
• 署名单位: National University of Singapore; Utah System of Higher Education; University of Utah
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01165-2
• 发表日期: 2023
• 页码: 1-78
• 关键词: representations; g(2); conjecture; series

摘要

We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is the exceptional group G(2). We prove the Howe duality conjecture for these dual pairs and a dichotomy theorem, and determine explicitly the theta lifts of all non-cuspidal representations.