Theta lifting for loop groups
Webin terms of the LLC; similarly, in [AG17], Atobe-Gan described the theta lifts of tempered representations in terms of the LLC. In this paper, we “turn the table around”, namely, imitating the prediction of Prasad conjecture, we construct a Vogan version LLC for unitary groups. We also write a parallel paper [CZ21], WebKey group-theoretic feature: De nition (Howe) Suppose G and G0are reductive subgroups of a symplectic group Sp(W) and each is the full centralizer of the other in Sp(W). Then (G;G0) is a reductive dual pair. Then one can produce a (global) theta corrrespondence by restricting a theta function on (the double cover of) Sp(W) to the embedded image of
Theta lifting for loop groups
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WebThe properties of these theta lifts have been extensively studied, and in particular the question of when theta lifts are not identically zero is known to be related to special values of automorphic L-functions. More precisely, assume that f generates an irreducible cuspidal automorphic representation ˇˆA 0(Sp 4;F). One can interpret the ... WebA generalization of Weil representation for loop symplectic groups was con-structed by one of us in [11]. As in the finite dimensional case, the Weil representation for the loop group Sp2n (F((t))) is a projective representation, and it gives rise a central extension Sp 2n (F((t))) of the loop group Sp2n (F((t))) which we call the metaplectic ...
Webin terms of the LLC; similarly, in [AG17], Atobe-Gan described the theta lifts of tempered representations in terms of the LLC. In this paper, we “turn the table around”, namely, … Webmetaplectic cover of the corresponding KacMoody group constructed by Patnaik- -Puskas. In the second work, we computed the theta lifting of (GLthe 𝑛𝑛,GL𝑛𝑛) dual pair of loop groups, starting from a function induced by a classical cuspidal automorphic form GL𝑛𝑛, and we explain the result as a certain on Eisenstein series ...
WebTHETA LIFTING FOR LOOP GROUPS DONGWEN LIU AND YONGCHANG ZHU∗ Abstract. In this paper we study the theta lifting for loop groups and extend the classical tower … WebThis leads to the idea of monodromy. For example, if p: S 1 → S 1 is the double cover p ( e i θ) = e i 2 θ then the path e i π t lifts the loop e i 2 π t . where γ ~ is the unique lift of γ starting at y . If γ 1 ≃ γ 2 then σ γ 1 = σ γ 2 . This will follow from the homotopy lifting lemma below.
WebIn 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 …
WebON THE NIWA-SHINTANI THETA-KERNEL LIFTING OF MODULAR FORMS BARRY A. CIPRA Modular forms of half-integral weight are of intrinsic interest: many of the functions of classical number theory transform under a matrix group with half-integral weight. The aim of this paper is to refine some results and techniques which have been introduced to study ... roll back the clock dinosaur movieWebMar 26, 2024 · The theta lifting is defined as a correspondence between representations of the two groups in a reductive dual pair in terms of the restriction of the Weil … rollback temporishttp://www.numdam.org/item/AST_2010__332__369_0/ roll back that stone lyricsWebJan 1, 2024 · Keywords: 22E55 / 22E67 / cusp forms / Loop groups / Theta lifting / Weil representations rollback tie down strapsWebSep 28, 2024 · The Orbit method (or Kirillov’s method, or method of coadjoint orbits) is a method in geometric representation theory concerned with identifying unitary representations of Lie groups with the canonical G - actions on spaces of sections of certain line bundles over coadjoint orbits of the Lie group. In terms of quantum physics this … outboard motor reliability ratingsWebDouble loop, which means that each integration box is equipped with a target surface on both sides, and the laser (two) of each integration box emits laser beams to the target surface of adjacent equipment on both sides, and each target surface receives the laser beam emitted by the adjacent side integrated box, thus forming a forward loop and a … rollback throttle cableWebMar 26, 2024 · The theta lifting is defined as a correspondence between representations of the two groups in a reductive dual pair in terms of the restriction of the Weil representation [47]. In fact, it is shown that this correspondence is one-to-one by Howe himself [20] in the real case and by Gan–Takeda [16] in the p -adic case, following earlier works of Howe [19] … outboard motor rental ontario