Theta lift
WebMar 26, 2024 · Namely, we find a global theta lift such that • at one real place, its localization is the theta lift of an arbitrary (limit of) discrete series representation; • at another real place, its localization is the theta lift of a discrete series representation with sufficiently regular infinitesimal character, which is determined explicitly by ... WebSep 17, 2014 · Our first main result is that if ρ is unitarizable, then except for one special case, the full local theta lift ρ′ = Θ(ρ) is equal to the local theta lift θ(ρ). Thus excluding …
Theta lift
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WebThe Borcherds lift Lecture 7 Charlotte Chan March 14, 2016 These are rough notes of a lecture in which we explain how to de ne the Borcherds lift from the regularized theta lift … Webthe theory of theta correspondence is to show that the lift Θ n(V σ)doesnotvanish. B. Roberts characterizes the global non-vanishing of the theta lift in terms of the local counterpart θ n(σ v). To be more precise, in [R4], Roberts proves that for m 2 ≤ n the theta lift does not vanish if and only if the local theta lift of each local ...
WebAs a typical example, we examine the theta lift of a holomorphic discrete series representation with a scalar extreme Kf0-type. Let ˇ0 hol be a holomorphic discrete series representation of Gf0= U(p;q) ˘.Al-though ˇ0 hol itself is fairly well understood, it is not so for its theta lift (ˇ0 hol). By the general arguments of Adams [1, x5 ... http://www.math.tifr.res.in/~dprasad/dp.pdf
WebJul 22, 2016 · On two arithmetic theta lifts. Stephan Ehlen, Siddarth Sankaran. Our aim is to clarify the relationship between Kudla's and Bruinier's Green functions attached to special cycles on Shimura varieties …
WebSection 3, after reviewing basics of both global and local theta lifting of groups of isometries, we give a proof of Theorem 1.0.1. In Section 4, we review basics of both global and local theta lifting of groups of similitudes. In Section 5, we will explic-itly compute the unrami ed local theta lift from GO(4) to GSp(1). Then nally,
Webtheta liftings. Roughly speaking, for each place v of F, the local theta lifting relates irreducible admissible representations of Gv and G0 v. Similarly the global theta lifting relates automorphic forms on the two groups. We consider the very special case in which dimE V = dimE W = 1. In this case, G »= G0 = U(1) = E1, where E1 is the kernel ... hjulgatan 4WebA Converse Theorem and the Saito-Kurokawa Lift 351 Proof. If `is a cusp form;this follows from [KS;pp. 197;207] where gis computed as a theta lift of `and is in fact a Maass cusp form of weight 1/2;so ¢1=2 gC(1=4C(r=2)2)gD0 where ¢1=2 Dy 2(@2 xC@ 2 y)¡(1=2)iy@x: If `DE(z;1=2Cir);the theorem follows from the next lemma;part of which is a fali szappanadagolóWebJun 16, 2024 · In this paper, we study a new lifting of automorphic representations using the theta representation $\Theta$ on the $4$-fold cover of the symplectic group, … hjulhamnsgatan 3bWebMay 23, 2016 · On a theta lift related to the Shintani lift. Claudia Alfes-Neumann, Markus Schwagenscheidt. We study a certain theta lift which maps weight to weight harmonic … fali száritóWebTheta correspondence. In mathematics, the theta correspondence or Howe correspondence is a mathematical relation between representations of two groups of a reductive dual pair. The local theta correspondence relates irreducible admissible representations over a local field, while the global theta correspondence relates irreducible automorphic ... hjulbalansering i motalaWebstudy the arithmetic properties of the theta-lifts in either direction. This issue was however considered by Shimura [32], who showed that (for suitable choices of theta function) the theta lift from SLg 2 to PB£ is algebraic and further, in the opposite direction, there is a canonical transcendental period modulo which the theta lift is ... hjulbalanseringWeb2. Generalities on theta cocycles and theta symbols 4 3. Analytic theta-cocycles 10 4. Meromorphic theta-symbols 25 5. Lifting obstructions 29 6. Generating series 38 Appendix A. The parallel with Mumford’s p-adic theta functions 41 References 43 1. Introduction Let pbe a rational prime and let H pdenote Drinfeld’s p-adic upper half plane ... hjulmakaregatan