Branching of metaplectic representation of 𝑆𝑝(2,ℝ) under its principal 𝕊𝕃(2,ℝ)-subgroup

Zhang, GenKai

doi:10.1090/ert/609

Represent. Theory

2022

DOI: 10.1090/ert/609

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Branching of metaplectic representation of 𝑆𝑝(2,ℝ) under its principal 𝕊𝕃(2,ℝ)-subgroup

GenKai Zhang

Abstract: We study the branching problem of the metaplectic representation of S p ( 2 , R ) Sp(2, \mathbb R) under its principle subgroup S L ( 2 , R ) SL(2, \mathbb R) . We find the complete decomposition.

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The Plancherel formula of Fourier integral operators: The case of Sp(1,1)

Jia,

Fan

2023

Int. J. Wavelets Multiresolut Inf. Process.

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In this paper, we consider the Plancherel formula for Fourier integral operator on the space [Formula: see text], where [Formula: see text] is the quaternion skew field. By using the metaplectic representations of a noncompact classical dual pair [Formula: see text] and combining with the Plancherel formula of Poisson transform, we obtain the direct integral decomposition of all irreducible unitary representations of Fourier integral operator.

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The Plancherel formula of Fourier integral operators: The case of Sp(1,1)

Jia,

Fan

2023

Int. J. Wavelets Multiresolut Inf. Process.

View full text Add to dashboard Cite

show abstract

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Branching of metaplectic representation of 𝑆𝑝(2,ℝ) under its principal 𝕊𝕃(2,ℝ)-subgroup

Abstract: We study the branching problem of the metaplectic representation of S p ( 2 , R ) Sp(2, \mathbb R) under its principle subgroup S L ( 2 , R ) SL(2, \mathbb R) . We find the complete decomposition.

Cited by 1 publication

References 20 publications

The Plancherel formula of Fourier integral operators: The case of Sp(1,1)

The Plancherel formula of Fourier integral operators: The case of Sp(1,1)

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