Multiplicity formulas for discrete series representations in

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• 作者：Satoshi Wakatsuki
• 关键词：Multiplicity formula ; The split symplectic group of rank 2 ; Discrete series representation ; Arthur?s L2L2-Lefschetz trace formula ; Dimension formula ; Siegel cusp form ; Automorphic representation
• 刊名：Journal of Number Theory
• 出版年：2013
• 出版时间：October, 2013
• 年：2013
• 卷：133
• 期：10
• 页码：3394-3425
• 全文大小：448 K

文摘

Let denote the split symplectic group of rank 2 over . Fix a prime p. Let be a parahoric subgroup of . An arithmetic subgroup ¦£ is defined by , where . In this paper, we calculate Arthur?s -Lefschetz trace formula for in order to obtain an explicit formula for multiplicities of discrete series and some non-tempered unitary representations in the discrete spectrum of for each such ¦£. From them we derive explicit multiplicity formulas for large discrete series, which are our main results. The multiplicity formulas are applied to a study on numbers of cuspidal automorphic representations of .