37 citations · 65 across the 13 of their papers we have counts for
15 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…
Mirror symmetry for circle compactified 4d SCFTs
Peng Shan, Dan Xie, Wenbin Yan
We propose a mirror symmetry for 4d superconformal field theories (SCFTs) compactified on a circle with finite size. The mirror symmetry involves vertex operator al…
A geometric realization of the center of the small quantum group
Roman Bezrukavnikov, Pablo Boixeda Alvarez, Peng Shan +1
We propose a new geometric model for the center of the small quantum group using the cohomology of certain affine Springer fibers. More precisely, we establish an isomorphism betwe…
On the cohomology of Calogero-Moser spaces
Cédric Bonnafé, Peng Shan
We compute the equivariant cohomology of smooth Calogero-Moser spaces and some associated symplectic resolutions of symplectic quotient singularities.
Femtosecond dynamics of correlated many-body states in C fullerenes
Sergey Usenko, Michael Schüler, Armin Azima +7
Fullerene complexes may play a key role in the design of future molecular electronics and nanostructured devices with potential applications in light harvesting using organic solar…
On the center of quiver-Hecke algebras
P. Shan, M. Varagnolo, E. Vasserot
We compute the equivariant cohomology ring of the moduli space of framed instantons over the affine plane. It is a Rees algebra associated with the center of cyclotomic degenerate…
Categorifications and cyclotomic rational double affine Hecke algebras
Raphael Rouquier, Peng Shan, Michela Varagnolo +1
Varagnolo and Vasserot conjectured an equivalence between the category O for CRDAHA's and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As ap…
Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA
Peng Shan, Michela Varagnolo, Eric Vasserot
We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensi…
Graded decomposition matrices of v-Schur algebras via Jantzen filtration
Peng Shan
We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirm…
Canonical bases and affine Hecke algebras of type D
Peng Shan, Michela Varagnolo, Eric Vasserot
We prove a conjecture of Kashiwara and Miemietz on canonical bases and branching rules of affine Hecke algebras of type D. The proof is similar to the proof of the type B case.
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
Peng Shan
We define the i-restriction and i-induction functors on the category O of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism clas…