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R-Group and Multiplicity in Restriction for Unitary Principal Series of GSpin and Spin

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Geometry, Algebra, Number Theory, and Their Information Technology Applications (GANITA 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 251))

Abstract

We study a relationship between the Knapp–Stein R-group and the multiplicity in the restriction for the case of unitary principal series of the p-adic split general spin groups to the split spin groups. An equality between the multiplicity and another multiplicity occurring in the corresponding representations of Knapp–Stein R-groups is established and applied to formulate the multiplicity in restriction in terms of information from the R-groups.

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Acknowledgements

We would like to express our appreciation to Kumar Murty for his continual contributions to our field. Also, we wish to thank the referee for the valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University, Carbondale, IL, 62901-4408, USA

    Dubravka Ban & Kwangho Choiy

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-2067, USA

    David Goldberg

Authors
  1. Dubravka Ban
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  2. Kwangho Choiy
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  3. David Goldberg
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Correspondence to David Goldberg .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB, Canada

    Amir Akbary

  2. Institute of Mathematical Sciences, Chennai, Tamil Nadu, India

    Sanoli Gun

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Ban, D., Choiy, K., Goldberg, D. (2018). R-Group and Multiplicity in Restriction for Unitary Principal Series of GSpin and Spin. In: Akbary, A., Gun, S. (eds) Geometry, Algebra, Number Theory, and Their Information Technology Applications. GANITA 2016. Springer Proceedings in Mathematics & Statistics, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-319-97379-1_4

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