仿射李代数的奇异模及其在不规则WZNW共形块中的应用

Opers with irregular singularity and spectra of the shift of argument subalgebra

The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA/0612798. We prove that generically their action on finite-dimensional modules is diagonalizable and their joint spectra are in bijection with the set of monodromy-free opers for the Langlands dual group of G on the projective line with regular singularity at one point and irregular singularity of order two at another point. We also prove a multi-point generalization of this result, describing the spectra of commutin…

Chiral algebra of Argyres-Douglas theory from M5 brane

We study chiral algebras associated with Argyres-Douglas theories engineered from M5 brane. For the theory engineered using 6d $(2,0)$ type $J$ theory on a sphere with a single irregular singularity (without mass parameter), its chiral algebra is the minimal model of W algebra of $J$ type. For the theory engineered using an irregular singularity and a regular full singularity, its chiral algebra is the affine Kac-Moody algebra of $J$ type. We can obtain the Schur index of these theories by computing the vacua character of the corresponding chiral algebra.

Classification de modules aux différences filtrés isogradués

The local analytic classification of irregular linear q-difference equations (Ramis-Sauloy-Zhang) involves the classfication of filtered q-difference modules with a prescribed associated graded module. We prove in a more general setting the existence for this problem of a moduli scheme which is an affine space. ----- La classification analytique locale des equations aux q-differences irregulieres se ramene a la classification de modules aux q-differences filtres a gradue fixe. Nous degageons ici des hypotheses generales qui assurent l'existence d'un schema de modules pour ce probleme, qui soit…

不规则联络的扭曲顶点代数模：一个案例研究

Twisted vertex algebra modules for irregular connections: A case study

本文以辛费米子顶点超代数和 triplet 顶点代数为案例，研究其关于不规则联络的 twisted 模，证明表示为 Whittaker 模直和，并揭示其与几何 Langlands 对应的联系。

野轨道与广义奇点模：分层与量子化

Wild orbits and generalised singularity modules: stratifications and quantisation

本文研究截断规范轨道的分层结构与量子化，通过不规则奇点连接 germ 的主部，计算稳定子并展示其连通性，同时通过变形量子化非通用轨道，扩展了奇点模的应用。

Compatibility of the Feigin-Frenkel Isomorphism and the Harish-Chandra Isomorphism for jet algebras

Let $\fg$ be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra $\fh$ and Weyl group $W$. Let $\fg_n$ denote the Lie algebra of $n$-jets on $\fg$. A theorem of Rais and Tauvel and Geoffriau identifies the centre of the category of $\fg_n$-modules with the algebra of functions on the variety of $n$-jets on the affine space $\fh^*/W$. On the other hand, a theorem of Feigin and Frenkel identifies the centre of the category of critical level smooth modules of the corresponding affine Kac-Moody algebra with the algebra of functions on the ind-scheme of opers for the Langlands …