On limit multiplicites of discrete series representations in spaces of automorphic forms
On limit multiplicites of discrete series representations in spaces of automorphic forms
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关于自守形式空间中离散级数表示的极限重数
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发表时间：
1986
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通讯作者：
L. Clozel
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作者：
L. Clozel
当然群F，则是G的算术子群。在这种情况下，似乎很自然地假定，当n = 1时，L2（F，G）的谱分解将近似于G的谱分解。特别地，设3是G的离散级数表示。若F是G的子群，设re（F，6）是G在L2（FG）上右平移表示中3的重数。选择G上的一个Haar测度dg;如果F是算术的，设v（FG）是FG对于dg诱导的测度的（有限）体积。设d（3）是测度dg的形式度3。
Of course the groups F, are then arithmetic subgroups of G. In this situation, it seems natural to assume that, as n-+ ~ , the spectral decomposition of L2(F,G) will approximate that of G. In particular, let 3 be a discrete series representation of G. If F is a subgroup of G, let re(F, 6) be the multiplicity of 3 in the representation of G, by right translations, on L2(FG). Choose a Haar measure dg on G; if F is arithmetic, let v(FG) be the (finite) volume of FG for the measure induced by dg. Let d(3) be the formal degree of 3 for the measure dg.