TY - JOUR

T1 - Representations associated to small nilpotent orbits for real spin groups

AU - Barbasch, Dan

AU - Tsai, Wan Yu

N1 - Publisher Copyright:
© 2018 Heldermann Verlag.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Nilpotent orbits

KW - Spin groups

KW - Unipotent representations

UR - http://www.scopus.com/inward/record.url?scp=85049859561&partnerID=8YFLogxK

M3 - 期刊論文

AN - SCOPUS:85049859561

SN - 0949-5932

VL - 28

SP - 987

EP - 1042

JO - Journal of Lie Theory

JF - Journal of Lie Theory

IS - 4

ER -