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Transactions of the American Mathematical Society

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A geometric formula for multiplicities of $ K$-types of tempered representations


Authors: Peter Hochs, Yanli Song and Shilin Yu
Journal: Trans. Amer. Math. Soc. 372 (2019), 8553-8586
MSC (2010): Primary 58J20; Secondary 22E46, 53D50, 53D20, 53C27
DOI: https://doi.org/10.1090/tran/7857
Published electronically: September 9, 2019
MathSciNet review: 4029704
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Additional Information

Peter Hochs
Affiliation: School of Mathematical Sciences, University of Adelaide, Adelaide, Australia
Email: peter.hochs@adelaide.edu.au

Yanli Song
Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri
Email: yanlisong@wustl.edu

Shilin Yu
Affiliation: School of Mathematical Sciences, Xiamen University, Fujian, China
Email: turingfish@gmail.com

DOI: https://doi.org/10.1090/tran/7857
Keywords: Tempered representation, equivariant index, multiplicity, geometric quantisation, reduction
Received by editor(s): May 24, 2018
Received by editor(s) in revised form: January 17, 2019, and March 24, 2019
Published electronically: September 9, 2019
Additional Notes: The first author was partially supported by the European Union, through Marie Curie fellowship PIOF-GA-2011-299300. He thanks Dartmouth College for funding a visit there in 2016.
The second author was supported by NSF grant 1800667.
The third author was partially supported by NSF grant 1564398.
Article copyright: © Copyright 2019 American Mathematical Society