Weyl groups, the Dirac inequality, and isolated unitary unramified representations
Weyl groups, the Dirac inequality, and isolated unitary unramified representations
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DOI：
10.1016/j.indag.2021.09.004
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发表时间：
2020-11
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影响因子：
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通讯作者：
D. Ciubotaru
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文献类型：
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作者：
D. Ciubotaru
在未分叉主级数的情况下，我给出了狄拉克不等式在确定孤立的么正表示和相关的“谱隙”方面的几个应用。该方法特别适用于将不可约的么正表示附加到朗兰兹对偶复李代数中的大的幂零轨道(如正则轨道、次正则轨道)上。这些结果可以看作是Salamanca-Riba关于具有强正则无穷小特征的不可约酉模(g，K)-模的分类的p-进的类似。
I present several applications of the Dirac inequality to the determination of isolated unitary representations and associated “spectral gaps” in the case of unramified principal series. The method works particularly well in order to attach irreducible unitary representations to the large nilpotent orbits (eg, regular, subregular) in the Langlands dual complex Lie algebra. The results could be viewed as a p-adic analogue of Salamanca-Riba’s classification of irreducible unitary (g, K)-modules with strongly regular infinitesimal character.