Journal of Lie Theory

no. 3
Local Coefficient Matrices and the Metaplectic Correspondence
Journal of Lie Theory, Volume 27 (2017) no. 3, pp. 657-670
The local coefficients of a principal series representation of a metaplectic group are defined in terms of the action of the standard intertwining operator on a canonical basis of the space of Whittaker functionals. By analyzing the nonsingularity of local coefficient matrices, we prove that for a certain class of unramified principal series representations of the metaplectic group, the local metaplectic correspondence preserves irreducibility.
DOI: 10.5802/jolt.964
Classification: 22D30, 11F32, 11F70, 11F85
Keywords: Principal series, automorphic forms, Shimura's correspondence 
@article{JOLT_2017_27_3_a2,
     author = {M. Budden and G. Goehle},
     title = {Local {Coefficient} {Matrices} and the {Metaplectic} {Correspondence}},
     journal = {Journal of Lie Theory},
     pages = {657--670},
     year = {2017},
     volume = {27},
     number = {3},
     doi = {10.5802/jolt.964},
     zbl = {1388.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.964/}
}
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M. Budden; G. Goehle. Local Coefficient Matrices and the Metaplectic Correspondence. Journal of Lie Theory, Volume 27 (2017) no. 3, pp. 657-670. doi: 10.5802/jolt.964

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