Weil Representation and Shimura Lifting

Xueli Wang () and Dingyi Pei ()
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Xueli Wang: South China Normal University, Department of Mathematics
Dingyi Pei: Guangzhou University, Institute of Mathematics and Information Science

Chapter Chapter 8 in Modular Forms with Integral and Half-Integral Weights, 2012, pp 265-319 from Springer

Abstract: Abstract Let V be an n-dimensional real vector space and V* be the dual space of V. Denote by B a bilinear form on (V × V*) × (V × V*) given by B(z1,z2) = (υ1,υ 2 * ) = υ 2 * =(υ1) for z1 = (υ1,υ 1 * ) and z2 = (υ2,υ 2 * ). Let A(V) be the Lie group with underlying manifold V × V* × T whose multiplication is given by $$ \left( {z,t} \right)\left( {z',t'} \right) = \left( {z + z',tt'e\left( {B\left( {z,z'} \right)} \right)} \right),\quad \forall z,z'\; \in V \times V^* ,t,t' \in T, $$ where T = {z ∈ ℂ||z| = 1} and e(z) = e2πiz.

Keywords: Modular Form; Eisenstein Series; Cusp Form; Theta Series; Cusp Point (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-29302-3_8

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