85 papers
This paper classifies deformation quantizations of smooth, admissible symplectic supervarieties by generalizing the Bezrukavnikov-Kaledin result to the super case, establishing a correspondence with their even reduced symplectic varieties, and applying these findings to nilpotent orbits of basic Lie superalgebras.
This paper constructs finite-dimensional quantum groups of type Super A at even roots of unity, classifies their ribbon structures to establish non-semisimple modular categories, and demonstrates that the resulting link invariants distinguish knots that are indistinguishable by the Jones or HOMFLYPT polynomials.
This paper establishes an explicit isomorphism between the equivariant nilpotent cohomological Hall algebra of one-dimensional sheaves on a surface resolving a Kleinian singularity and a completed positive half of the affine Yangian of the corresponding ADE Lie algebra, utilizing continuity theorems for -structures and multi-parameter Yangian definitions to characterize the algebra of cohomological Hecke operators.
This paper investigates the blowup phenomena of Toda systems, which generalize the Liouville equation via simple Lie algebras, by providing concrete examples of blowup masses that correspond to Weyl groups.
This paper overcomes the limitations of standard unitary designs in arbitrary qudit dimensions by introducing weighted state designs and a Clifford character randomized benchmarking protocol, while also establishing circuit complexity bounds and proving that spin-GKP codewords form state 2-designs whereas spin coherent states do not.