## Representations associated to small nilpotent orbits for complex Spin groups

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- by Dan Barbasch and Wan-Yu Tsai
- Represent. Theory
**22**(2018), 202-222 - DOI: https://doi.org/10.1090/ert/517
- Published electronically: October 25, 2018
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## Abstract:

This paper provides a comparison between the $K$-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type $D$. Precisely, let $G_0 =\operatorname {Spin}(2n,\mathbb {C})$ be the Spin complex group as a real group, and let $K\cong G_0$ be the complexification of the maximal compact subgroup of $G_0$. We compute $K$-spectra of the regular functions on some small nilpotent orbits $\mathcal {O}$ transforming according to characters $\psi$ of $C_{ K}(\mathcal {O})$ trivial on the connected component of the identity $C_{ K}(\mathcal {O})^0$. We then match them with the ${K}$-types of the genuine (i.e., representations which do not factor to $\operatorname {SO}(2n,\mathbb {C})$) unipotent representations attached to $\mathcal {O}$.## References

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## Bibliographic Information

**Dan Barbasch**- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850
- MR Author ID: 30950
- Email: barbasch@math.cornell.edu
**Wan-Yu Tsai**- Affiliation: Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan
- Address at time of publication: Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada
- MR Author ID: 821037
- Email: wtsai@uottawa.ca, wanyupattsai@gmail.com
- Received by editor(s): September 5, 2017
- Received by editor(s) in revised form: April 2, 2018
- Published electronically: October 25, 2018
- Additional Notes: The first author was supported in part by NSA Grant H98230-16-1-0006.
- © Copyright 2018 American Mathematical Society
- Journal: Represent. Theory
**22**(2018), 202-222 - MSC (2010): Primary 22E46, 22E47
- DOI: https://doi.org/10.1090/ert/517
- MathSciNet review: 3868568