Rigid Tensor Structure on Big Module Categories for Some W-(super)algebras in Type A
T Creutzig, R McRae, J Yang - Communications in Mathematical Physics, 2023 - Springer
We establish rigid tensor category structure on finitely-generated weight modules for the
subregular W-algebras of sl n at levels-n+ nn+ 1 (the B n+ 1-algebras of Creutzig–Ridout …
subregular W-algebras of sl n at levels-n+ nn+ 1 (the B n+ 1-algebras of Creutzig–Ridout …
On the structure of W-algebras in type A
T Creutzig, J Fasquel, AR Linshaw… - arXiv preprint arXiv …, 2024 - arxiv.org
We formulate and prove examples of a conjecture which describes the W-algebras in type A
as successive quantum Hamiltonian reductions of affine vertex algebras associated with …
as successive quantum Hamiltonian reductions of affine vertex algebras associated with …
[HTML][HTML] Quasi-lisse extension of affine sl2 à la Feigin–Tipunin
T Creutzig, S Nakatsuka, S Sugimoto - Advances in Mathematics, 2024 - Elsevier
We study the affine analogue FT p (sl 2) of the triplet algebra. We show that FT p (sl 2) is
quasi-lisse and the associated variety is the nilpotent cone of sl 2. We realize FT p (sl 2) as …
quasi-lisse and the associated variety is the nilpotent cone of sl 2. We realize FT p (sl 2) as …
Quantum Frobenius and modularity for quantum groups at arbitrary roots of 1
C Negron - arXiv preprint arXiv:2311.13797, 2023 - arxiv.org
We consider quantum group representations Rep (G_q) for a semisimple algebraic group G
at a complex root of unity q. Here we allow q to be of any order. We first show that the …
at a complex root of unity q. Here we allow q to be of any order. We first show that the …
Mirror Symmetry and Level-rank Duality for 3d Rank 0 SCFTs
T Creutzig, N Garner, H Kim - arXiv preprint arXiv:2406.00138, 2024 - arxiv.org
We introduce a family of 3d $\mathcal {N}= 4$ superconformal field theories that have zero-
dimensional Coulomb and Higgs branches and propose that the rational vertex operator …
dimensional Coulomb and Higgs branches and propose that the rational vertex operator …
Tensor categories of weight modules of at admissible level
T Creutzig - arXiv preprint arXiv:2311.10240, 2023 - arxiv.org
The category of weight modules $ L_k (\mathfrak {sl} _2)\text {-wtmod} $ of the simple affine
vertex algebra of $\mathfrak {sl} _2 $ at an admissible level $ k $ is neither finite nor …
vertex algebra of $\mathfrak {sl} _2 $ at an admissible level $ k $ is neither finite nor …
BGG Reciprocity for Generalized Weight Modules of Unrolled Restricted Quantum Groups at Roots of Unity
M Rupert - arXiv preprint arXiv:2402.03668, 2024 - arxiv.org
We consider the category of generalized weight modules over the unrolled restricted
quantum group $\overline {U} _q^ H (\mathfrak {g}) $ of a finite-dimensional simple complex …
quantum group $\overline {U} _q^ H (\mathfrak {g}) $ of a finite-dimensional simple complex …
Fibre functors and reconstruction of Hopf algebras
S Lentner, M Mombelli - Canadian Journal of Mathematics, 2023 - cambridge.org
The main objective of the present paper is to present a version of the Tannaka-Krein type
reconstruction Theorems: If F: B→ C is an exact faithful monoidal functor of tensor …
reconstruction Theorems: If F: B→ C is an exact faithful monoidal functor of tensor …
The non-semisimple Kazhdan-Lusztig category for affine at admissible levels
R McRae, J Yang - arXiv preprint arXiv:2312.01088, 2023 - arxiv.org
We show that Kazhdan and Lusztig's category $ KL^ k (\mathfrak {sl} _2) $ of modules for the
affine Lie algebra $\widehat {\mathfrak {sl}} _2 $ at an admissible level $ k $, equivalently …
affine Lie algebra $\widehat {\mathfrak {sl}} _2 $ at an admissible level $ k $, equivalently …