2022/07/31 by Jiajun Ma, Ma, Jia-Jun, Congling Qiu +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2208.00431
openalex publication_date 2022/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for type I dual pairs over finite fields. For the product of the pair of Hecke algebras under consideration, we show that there is a generic Hecke algebra module whose specializations at prime powers give the Hecke algebra modules and whose specialization at 1 can be explicitly described. As an application, we prove the conservation relation on the first occurrence indices for all irreducible representations. As another application, we generalize the results of Aubert-Michel-Rouquier and Pan on theta correspondence between the Harish-Chandra series.