Theta lifting for loop groups

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August undefined, 2024

WebMar 26, 2024 · We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as cohomologically induced representations in the weakly fair range. This extends a result of J.-S. Li in the case of … 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.

Extending the Theta Correspondence

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 ... Web3. 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 ... autobussen te koop

Mixed Arithmetic Theta Lifting for Unitary Groups SpringerLink

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 … 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 ... gaztelaniazko esamoldeak euskaraz

$[2111.09195] Theta liftings for $(\mathrm{GL}_n,\mathrm{GL}_n)$

arXiv:1808.05005v3 [math.RT] 8 Jun 2024

WebWorked closely with Marketing, Engineering, and other groups in the planning process to define business, process and resource requirements. Created use cases, customer flow diagrams and business ... WebLOCAL-GLOBAL NON-VANISHING OF THETA LIFTS 5577 case, Θ 1(V σ) is the space of an irreducible cuspidal representation Π such that Π∨ = τJL 1 = τJL 2. (2) If d =1and σ is extended from π = π(τ,χ), then the theta lift Θ 1(V σ) to GSp(1,A F) does not vanish if and only if τJL is the base change lift of an irreducible cuspidal automorphic representation τ … gaztelania euskara hiztegiaWebtheta 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 ... gaztelania

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Theta lifting for loop groups

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 ... WebAeroelasticity is the branch of physics and engineering studying the interactions between the inertial, elastic, and aerodynamic forces occurring while an elastic body is exposed to a fluid flow. The study of aeroelasticity may be broadly classified into two fields: static aeroelasticity dealing with the static or steady state response of an elastic body to a fluid …

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WebarXiv: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 … WebJan 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 …

WebJan 15, 2024 · In this article, we construct mixed generating functions of special cycles and mixed arithmetic theta lifting, and prove the product relation. We then formulate a conjecture on the arithmetic inner product formula for odd rank unitary groups, complementary to the even rank case previously formulated in the author’s thesis. WebMasters of Aeronautical Engineering Graduate. Masters thesis investigated sailplane winglet design optimisation using computational fluid dynamics including Gamma Re-Theta transition modelling. During my degree I undertook an industrial placement year, where I worked as part of the manufacturing simulation team at Wilde Analysis. This primarily …

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 ... 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 …

WebTheta lifting for loop groups - CORE Reader

WebCORE is not-for-profit service delivered by the Open University and Jisc. autobussen rotselaarWebAug 15, 2024 · Request PDF Theta lifting for loop groups In this paper we study the theta lifting for loop groups and extend the classical tower property established by S. Rallis to … gaztelan telefonoWebNov 17, 2024 · Download PDF Abstract: In this article we prove the theta liftings of a cusp form on the loop group $\mathrm{GL}_n$ induced from a classical cusp form for the loop … autobusy olympia olomoucWebJan 16, 2024 · In plain words, Big O notation describes the complexity of your code using algebraic terms. To understand what Big O notation is, we can take a look at a typical example, O (n²), which is usually pronounced “Big O squared”. The letter “n” here represents the input size, and the function “g (n) = n²” inside the “O ()” gives us ... autobusi uz tallinuWebTHETA 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 … gaztelania euskaraWebApr 13, 2024 · This solution gives pictorial view of theta beta definition used in blade gen tool. This will help designer to better understand the relation between two variables. Attachments: 1. 2057651 - Pictorial view of theta beta definition - BladeGen.pdf gaztelania elhuyarWebtheta lifts from orthogonal groups, see [30], [38]. By deﬁnition, our local liftings are another type of theta lift coming from SL(2, F v). What we will prove is an identity between local theta lifts on GSp(4,F v) coming from GO(X,F v), where X is an anisotropic four-dimensional quadratic space with discriminant 1, and others coming from SL(2, F autobuses yecla jumilla