2018/08/07 by Wan Chen, Lei Zhang, Wan, Chen +1
Mathematics · #22E35 #22E50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1808.02203
openalex publication_date 2018/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the local multiplicity problems of the analogy of the Ginzburg-Rallis model for the unitary group and the unitary similitude group cases. For the unitary similitude group case, by proving a local trace formula for the model, we are able to prove a multiplicity formula for all tempered representations, which implies that the summation of the multiplicities is equal to 1 over every tempered local Vogan L-packet. For the unitary group case, we also prove a multiplicity formula for all tempered representations which implies that the summation of the multiplicities is equal to 2 over every tempered local Vogan L-packet.