Representations associated to small nilpotent orbits for real spin groups

Dan Barbasch, Wan Yu Tsai

研究成果: 雜誌貢獻期刊論文同行評審

4 引文 斯高帕斯(Scopus)


The results in this paper provide a comparison between the K-structure of unipotent representations and regular sections of bundles on nilpotent orbits. Precisely, let G0 = Spin (a,b) with a + b = 2n, the nonlinear double cover of Spin(a,b), and let K = Spin(a,C) × Spin(b,C) be the complexification of the maximal compact subgroup of G0. We consider the nilpotent orbit Oc parametrized by [3 22k 12n 4k−3] with k > 0. We provide a list of unipotent representations that are genuine, and prove that the list is complete using the coherent continuation representation. Separately we compute K -spectra of the regular functions on certain real forms O of Oc transforming according to appropriate characters ψ under CK(O), and then match them with the K -types of the genuine unipotent representations. The results provide instances for the orbit philosophy.

頁(從 - 到)987-1042
期刊Journal of Lie Theory
出版狀態已出版 - 2018


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