Metaplectic correspondence

Abstract

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Theta distinguished representations, inflation and the symmetric square L-function

“…The metaplectic tensor product in the context of GL n has been studied by various authors [17,37,53,68,69]. Our definitions were motivated by the construction of Kable [37] (see Remark 2.2 below).…”

Metaplectic tensor products for irreducible representations

“…In an attempt to avoid this difficulty, a method of parabolic induction is proposed in §26.2 [4], in which M is replaced by a subgroup M B which is isomorphic to (an obvious quotient of) M B 1 × • • • × M B . Despite this nice decomposition, H. Sun ( §4 [13]) has pointed out that the centralizer of M B in M is not necessarily contained in the product of M B and the centre of G. As a result, the representation of M constructed in §26.2 [4] is not necessarily irreducible, as is claimed there. In other words, this metaplectic analogue for the usual tensor product representation may be reducible.…”

On Euler products associated with noncuspidal metaplectic forms

“…There are few other approaches towards the Shimura Correspondence, such as, as a case of the theta correspondence [17], [14], [7], use of Selberg's trace formulas [5], [6].…”