5 papers
Cyclotomic level maps and associated varieties of simple affine vertex algebras
Peng Shan, Wenbin Yan, Qixian Zhao
In this paper, we introduce and study two cyclotomic level maps defined respectively on the set of nilpotent orbits in a complex semi-simple Lie algebra $…
Monoidal categorification of genus zero skein algebras
Dylan G. L. Allegretti, Hyun Kyu Kim, Peng Shan
We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized -theoretic Coulomb br…
Modularity for -algebras and affine Springer fibres
Peng Shan, Dan Xie, Wenbin Yan
We construct a bijection between admissible representations for an affine Lie algebra at boundary admissible levels and fixed points in homogeneo…
Skein algebras and quantized Coulomb branches
Dylan G. L. Allegretti, Peng Shan
To a compact oriented surface of genus at most one with boundary, we associate a quantized -theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the…
Categorical action for finite classical groups and its applications: characteristic 0
Pengcheng Li, Peng Shan, Jiping Zhang
In this paper, we construct a categorical double quantum Heisenberg action on the representation category of finite classical groups , a…