On the wavefront sets associated with theta representations

Fan Gao; Wan Yu Tsai

doi:10.1007/s00209-021-02894-5

On the wavefront sets associated with theta representations

Fan Gao, Wan Yu Tsai

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study a conjectural formula for the maximal elements in the wavefront set associated with a theta representation of a covering group over p-adic fields. In particular, it is shown that the formula agrees with the existing work in the literature for various families of groups. We also recapitulate the results of an analogous formula in the archimedean case, which motivated the conjectural formula in the p-adic setting.

Original language	English
Journal	Mathematische Zeitschrift
Volume	301
Issue number	1
DOIs	https://doi.org/10.1007/s00209-021-02894-5
State	Published - May 2022

Keywords

Character expansion
Covering groups
Primitive ideals
Springer correspondence
Theta representation
Unipotent orbits
Wavefront sets

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10.1007/s00209-021-02894-5

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AB - We study a conjectural formula for the maximal elements in the wavefront set associated with a theta representation of a covering group over p-adic fields. In particular, it is shown that the formula agrees with the existing work in the literature for various families of groups. We also recapitulate the results of an analogous formula in the archimedean case, which motivated the conjectural formula in the p-adic setting.

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KW - Primitive ideals

KW - Springer correspondence

KW - Theta representation

KW - Unipotent orbits

KW - Wavefront sets

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On the wavefront sets associated with theta representations

Abstract

Keywords

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