Journal of the Ramanujan Mathematical Society

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Twisted Exterior Square Lift from GU(2,2)E/F to GL6/F


Affiliations
1 Dept. of Math., University of Toronto, Toronto, ON M5S 2E4, Canada
2 Dept. of Math., University of Iowa, Iowa City, IA 52242, United States
     

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Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F. We prove functoriality from globally generic cuspidal representations of GU(2, 2)(𝔸F ) to automorphic representations of GL6(𝔸F ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F, the twisted exterior square map reduces to the usual exterior square map from GL4(𝕔) to GL6(𝕔). We also discuss functoriality for the twisted symmetric fourth power map and discuss its relation with functoriality of the twisted exterior square.


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  • Twisted Exterior Square Lift from GU(2,2)E/F to GL6/F

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Authors

Henry H. Kim
Dept. of Math., University of Toronto, Toronto, ON M5S 2E4, Canada
Muthukrishnan Krishnamurthy
Dept. of Math., University of Iowa, Iowa City, IA 52242, United States

Abstract


Suppose E/F is a quadratic extension of number fields and GU(2, 2) is the quasi-split unitary similitude group attached to E/F. We prove functoriality from globally generic cuspidal representations of GU(2, 2)(𝔸F ) to automorphic representations of GL6(𝔸F ) corresponding to the twisted exterior square map on the dual side. For a split quadratic algebra E/F, the twisted exterior square map reduces to the usual exterior square map from GL4(𝕔) to GL6(𝕔). We also discuss functoriality for the twisted symmetric fourth power map and discuss its relation with functoriality of the twisted exterior square.