## Vogan duality for nonlinear type B

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- Represent. Theory
**15**(2011), 258-306 Request permission

## Abstract:

Let $\mathbb {G}=\mathrm {Spin}[4n+1]$ be the connected, simply connected complex Lie group of type $B_{2n}$ and let $G=\mathrm {Spin}(p,q)$ $(p+q=4n+1)$ denote a (connected) real form. If $q \notin \left \{0,1\right \}$, $G$ has a nontrivial fundamental group and we denote the corresponding nonalgebraic double cover by $\tilde {G}=\widetilde {\mathrm {Spin}}(p,q)$. The main purpose of this paper is to describe a symmetry in the set of genuine parameters for the various $\tilde {G}$ at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized Hecke modules and ultimately results in a character multiplicity duality for the genuine characters of $\tilde {G}$.## References

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## Additional Information

**Scott Crofts**- Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
- Received by editor(s): August 13, 2009
- Received by editor(s) in revised form: August 5, 2010
- Published electronically: March 24, 2011
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**15**(2011), 258-306 - MSC (2010): Primary 20G05
- DOI: https://doi.org/10.1090/S1088-4165-2011-00398-8
- MathSciNet review: 2788895