A proof of the Howe duality conjecture
英文摘要：
We give a proof of the Howe duality conjecture in local theta correspondence for symplectic-orthogonal or unitary dual pairs in arbitrary residual characteristic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
On the Howe duality conjecture in classical theta correspondence
We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for any nonarchimedean local field of characteristic not 2 and in arbitrary residual characteristic.
math.NTmath.RT
On the lattice model of the Weil representation and the Howe duality conjecture
The lattice model of the Weil representation over non-archimedean local field $F$ of odd residual characteristic has been known for decades, and is used to prove the Howe duality conjecture for unramified dual pairs when the residue characteristic of $F$ is odd. In this paper, we will modify the lattice model of the Weil representation so that it is defined independently of the residue characteristic. Although to define the lattice model alone is not enough to prove the Howe duality conjecture for even residual characteristic, we will propose a couple of conjectural lemmas which imply the Howe…
math.NTmath.RT
某些强 tempered 球面簇的 BZSV 对偶
BZSV Duality for Some Strongly Tempered Spherical Varieties
本文围绕 BZSV 相对 Langlands 对偶提出两族相对迹公式比较，统一既有结果，并证明强 tempered 球面簇在 p-adic 情形的基本引理与光滑转移，同时推广 Whittaker 周期猜想。
math.NTmath.RT
Hirose 对偶猜想的证明
A proof of Hirose's duality conjecture
Nagahama Institute of Bio-Science and Technology（米原生物科学技术研究所）
本文利用对称终止的 ${}_{4}\phi_{3}$ 连接子证明了 Hirose 关于四穿孔射影线上迭代积分 $q$-离散化的对偶猜想。
math.NT
局部相对朗兰兹对偶的分类化
Categorification of local relative Langlands duality
The University of Tokyo（东京大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
本文在范畴化局部朗兰兹对应框架内，验证了归一化周期猜想对于伊瓦萨-塔特和海克周期的情况，假设存在GL₂的范畴化局部朗兰兹对应并具有艾森斯坦兼容性。
math.NTmath.RT
Alternating Multiple $T$-Values: Weighted Sums, Duality, and Dimension Conjecture
In this paper, we define some weighted sums of the alternating multiple $T$-values (AMTVs), and study several duality formulas for them by using the tools developed in our previous papers. Then we introduce the alternating version of the convoluted $T$-values and Kaneko-Tsumura $ψ$-function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $\Q$-vector space generated by the AMTVs of any fixed weight $w$ and provide some evidence for the conjecture that their dimensions $\{d_w\}_{w\ge 1}$ form the tribonacci sequence 1, 2, 4, 7, 13, ....
math.NT
更多相关论文收起更多论文
广义Whittaker模型作为相对Langlands对偶的实例II: Plancherel密度与全局周期
Generalised Whittaker models as instances of relative Langlands duality II: Plancherel density and global periods
National University of Singapore（新加坡国立大学）
本文研究了一类广义Whittaker模型在相对Langlands对偶框架下的局部Plancherel密度数值猜想及其在全局周期猜想中的应用。
math.NTmath.RT
Hida duality and the Iwasawa main conjecture
The central result of this paper is a refinement of Hida's duality theorem between ordinary Lambda-adic modular forms and the universal ordinary Hecke algebra. Specifically, we give a necessary condition for this duality to be integral with respect to particular submodules of the space ordinary Lambda-adic modular forms. This refinement allows us to give a simple proof that the universal ordinary cuspidal Hecke algebra modulo Eisenstein ideal is isomorphic to the Iwasawa algebra modulo an ideal related to the Kubota-Leopoldt p-adic L-function. The motivation behind these results stems from Oht…
math.NT
Howe duality and dichotomy for exceptional theta correspondences
We study three exceptional theta correspondences for p-adic groups, where one member of the dual pair is the exceptional group G2. We prove the Howe duality conjecture for these dual pairs and a dichotomy theorem, and determine explicitly the theta lifts of all non-cuspidal representations.
math.NTmath.RT
一般低次超曲面和庞加莱对偶的几何马林猜想的逆
A converse to geometric Manin's conjecture for general low degree hypersurfaces and Poincaré duality
Department of Mathematics, Columbia University（哥伦比亚大学数学系）
该研究通过高亏分数的圆法推广，证明了对于一般低次超曲面，不存在增加Fujita不变量的累积映射，从而在特定范围内建立了这些模空间的庞加莱对偶性。
math.AGmath.NT
周期的几何朗兰兹对偶
Geometric Langlands duality for periods
本文研究Ben-Zvi--Sakellaridis--Venkatesh关于几何朗兰兹对偶中周期与L-函数关系的范畴化猜想，并通过导出傅里叶分析和手征代数在低秩例子中提供证据。
math.AGmath.NTmath.RT
关于去掉四个一般点的P¹上迭代q积分的猜想对偶性
Conjectural duality for iterated $q$-integrals on $\mathbb{P}^{1}$ minus four generic points
Kagoshima University（鹿儿岛大学）
本文提出一个关于经典对偶性的q类比猜想，通过引入带有位置依赖的q位移参数的迭代q积分，定义在六对字母上的函数，并证明其在自然反自同构下保持不变，同时将其与Yamamoto的单变量多重q-polylogarithms对偶性相关联。
math.NT
Langlands duality for skein modules of 3-manifolds
I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases where the conjecture is confirmed. The proofs in these cases combine the representation theory of double affine Hecke algebras and a new 1-form symmetry structure on skein modules related to electric-magnetic duality. This note is an expansion of my talk given at String Math 2022 in Warsaw, and is submitted to the String Math 2022 Proceedings publication.
math.GTmath.NTmath.QA
关于Nahm和的Zagier对偶猜想的反例
Counterexamples to Zagier's Duality Conjecture on Nahm Sums
针对Nahm问题中Zagier提出的模形式Nahm和的对偶也为模形式的猜想，构造出秩为4的模形式Nahm和反例，其对偶不具备模形式性质，从而证伪该对偶猜想。
math.COmath.NT
Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality
We present a conjecture describing new long range correlations among the Riemann zeros leading to 3 principal features: (i) The spectral auto-correlation is invariant w.r.t. the averaging window. (ii) Resurgence occurs wherein the lowest zeros appear in all auto-correlations. (iii) Suitably defined correlations lead to predictions (prophecy) of new zeros. This conjecture is supported by analytical arguments and confirmed by numerical calculations using 10^{22} zeros computed by Odlyzko. The results lead to a self-duality of the Riemann spectrum similar to the quantum-classical duality observed…
math-phmath.MPmath.NT
Formal duality in finite cyclic groups
The notion of formal duality in finite Abelian groups appeared recently in relation to spherical designs, tight sphere packings, and energy minimizing configurations in Euclidean spaces. For finite cyclic groups it is conjectured that there are no primitive formally dual pairs besides the trivial one and the TITO configuration. This conjecture has been verified for cyclic groups of prime power order, as well as of square-free order. In this paper, we will confirm the conjecture for other classes of cyclic groups, namely almost all cyclic groups of order a product of two prime powers, with fini…
math.CAmath.COmath.NT
