Theta lifting for loop groups
http://www.homepages.ucl.ac.uk/~ucahjde/tg/html/cov-04.html 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
Did you know?
WebTheta lifting for loop groups - CORE Reader Websymplectic groups in orthogonal towers. In particular, their results imply that every nongeneric supercuspidal representations of GSp 4(F) can be obtained as a theta lift from the anisotropic GSO 4;0. The third is a recent result of Henniart [Hen10] which shows that the local Langlands correspondence for GL n respects the twisted exterior ...
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 ... Webmetaplectic loop group of SP2n, in which the above group Gand the lifting of SLn(R((t))) form a commuting pair. Our construction can be viewed as the theta lifting of characters of G to representations of the central extension of SLn(R((t))). Since this connection is for-
WebNov 15, 1998 · 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 … 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 …
WebMar 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] …
WebNov 17, 2024 · Download Citation Theta liftings for $(\\mathrm{GL}_n,\\mathrm{GL}_n)$ type dual pairs of loop groups In this article we prove the theta liftings of a cusp form on … grammar school in high wycombeWeb3. Theta lifts 15 3.1. Weil representations15 3.2. The archimedean case16 3.3. Doubling zeta integrals17 3.4. A duality property of doubling zeta integrals19 4. Arithmetic theta lifts23 4.1. Shimura varieties attached to incoherent unitary groups23 4.2. Hecke actions24 4.3. Generating series25 4.4. Pullback of generating series27 4.5 ... grammar school in medwayWebformal loop group and a highest weight representation of the underlying affine Kac–Moody algebra. In the case that the element has a polynomial representative, we can prove our lattices are theta-finite in the sense of Bost, allowing us to attach to each of our lattices a well-defined theta-like function. Contents 1. grammar school in croydonWebarXiv:1808.05005v3 [math.RT] 8 Jun 2024 THETA LIFTING FOR LOOP GROUPS DONGWEN LIU AND YONGCHANG ZHU∗ Abstract. In this paper we study the theta lifting for loop … grammar school in lincolnshireWebA 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 ... china silicone ice trays factoryWebJan 1, 2014 · We introduce a categorical framework for the study of representations of G(F), where G is a reductive group, and F is a 2-dimensional local field, i.e. F = K((t)), where K is … grammar school in nottinghamWebThe theta-kernel Aut G, H on Bun G × Bun H yields theta-lifting functors F G: D (Bun H) → D (Bun G) and F H: D (Bun G) → D (Bun H) between the corresponding derived categories. We describe the relation of these functors with Hecke operators. china silicone ice cube trays manufacturers