Theta lifting for loop groups

2018/08/15 by Dongwen Liu, Liu, Dongwen, Yongchang Zhu +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1808.05005

Final version, to appear in Duke Math. J

arxiv created 2021/09/16 · arxiv updated 2021/09/17

Abstract

In this paper we study the theta lifting for loop groups and extend the classical tower property established by S. Rallis to the loop setting. As an application we obtain cusp forms on loop groups, and we give the first example where the cusp forms constructed using this method are nonvanishing.

Related

• Theta liftings for (GL_n,GL_n) type dual pairs of loop groups
• The tower property on the genericity of global theta lifts
• Some local-global non-vanishing results for theta lifts from orthogonal groups
• On the Whittaker range of the generalized metaplectic theta lift
• On the Siegel-Weil Theorem for Loop Groups (II)