Tame twistings and $Θ$-data

Zhao, Yifei

doi:10.48550/arxiv.2004.09671

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Conjecture 14 (Categorical Geometric Langlands Correspondenc...1

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“…One can additionally include in the twisting datum an extension of the canonical sheaf ω C by O C ⊗z * . The meaning of this full twisting datum in the geometric Langlands program has been studied by Zhao [Zha17;Zha20]. This twisting family is extended further in the metaplectic Langlands correspondence of Gaitsgory and Lysenko [GL18].…”

Section: Conjecture 14 (Categorical Geometric Langlands Correspondenc...mentioning

confidence: 99%

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory

Elliott,

Yoo

2020

Preprint

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We describe the family of supersymmetric twists of N = 4 super Yang-Mills theory using derived algebraic geometry, starting from holomorphic Chern-Simons theory on N = 4 super twistor space. By considering an ansatz for categorical geometric quantization of the family of further twists of a fixed holomorphic twist, we give a quantum field-theoretic synthesis of the categories of twisted D-modules occuring in the quantum geometric Langlands correspondence.

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Section: Conjecture 14 (Categorical Geometric Langlands Correspondenc...mentioning

confidence: 99%

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory

Elliott,

Yoo

2020

Preprint

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Twisted Whittaker category on affine flags and category of representations of mixed quantum group

Yang¹

2021

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We prove the twisted Whittaker category on the affine flag variety and the category of representations of the mixed quantum group are equivalent.(see (0.14) in [GL1]). A naive attempt is to use the Jacquet functor F KD from F l G to Gr T , namely, we !-pullback from F l G to F l B − and then take * -direct image to Gr T = F l T . However, the problem is that the image does not have a Ω W hit,Lus κ factorization module structure (except when κ is generic). For a coweight λ, the λ-component of

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Tame twistings and $Θ$-data

Cited by 2 publications

References 16 publications

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory

Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory

Twisted Whittaker category on affine flags and category of representations of mixed quantum group

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