Alphabeta MathQuantum Drinfeld Sokolov And W Algebras
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2 · Logical flowchart
3 · Items
Definition
Finite-dimensional simple complex Lie algebra
Lemma
Off-critical affine Shapovalov factors and strong linkage
Lemma
Integrable affine WZW highest-weight modules are graded and restricted
Definition
Fixed-coordinate sphere Virasoro block family
Lemma
Virasoro Verma modules have a unique simple highest-weight quotient
Definition
Nilpotent element in a finite-dimensional Lie algebra
Lemma
The root system of a simple Lie algebra is irreducible
Lemma
Affine semiregular tilting and the admissible BGG resolution
Definition
Integrable WZW insertions on a punctured sphere
Lemma
Stress-tensor Ward identity on the sphere
Definition
Root normalization and dual data for principal W levels
Theorem
Jacobson-Morozov triple for a nilpotent element
Lemma
Finite affine polarizations and their canonical determinants
Definition
Fixed-coordinate WZW sphere current coinvariants
Lemma
Pairwise Casimirs satisfy infinitesimal braid relations
Definition
Unordered WZW top fiber with label assignments
Definition
Nondegenerate principal admissible affine level
Definition
Good grading and isotropic data for affine W-algebra reduction
Definition
Slodowy slice associated to a nilpotent element
Lemma
Exact two-sided Wakimoto resolution for an admissible affine module
Lemma
Current Ward identity for WZW sphere coinvariants
Definition
Affine W algebra by quantum Drinfeld-Sokolov reduction
Lemma
Principal-level arithmetic implies affine vacuum admissibility
Lemma
Principal gauge torsor and equivariant quotient constraint acyclicity
Theorem
BRST vanishing and PBW theorem for affine W algebras
Lemma
Affine Zhu quotient and G-integrable admissible descent
Lemma
Exact classical principal reduction on equivariant arc modules
Lemma
Integral-root congruences and actual affine quotient-module transports
Lemma
Quantum principal quotient Li tails and strict degree-zero reduction
Lemma
Universal principal Whittaker equivalence and arbitrary central coefficients
Lemma
Admissible affine sl2 vacuum null polynomial
Lemma
Exact principal reduction of Harish–Chandra bimodules and its Kazhdan filtration
Lemma
Exact finite Whittaker coinvariants and Verma dual top homology
Lemma
Parabolic BRST restriction through the simple rank-one affine vacuum
Lemma
Natural principal VOA Zhu and actual-ideal BRST comparison
Lemma
Nonzero C2 symbol of the actual admissible affine sl2 vacuum null state
Theorem
Admissible affine VOA modules in category O
Lemma
Corrected principal BRST induced complexes and minus reduction of affine Vermas
Lemma
Signed principal spectral-flow bridge to the intrinsic contragredient
Lemma
Actual admissible affine nilcone and nonzero principal C2-finite reduction
Lemma
Principal central reduction, regular deformation transport and semisimple minimal-series tops
Theorem
KZ equations for WZW conformal blocks on the sphere
Theorem
BPZ equation from a Virasoro level-two null vector
Lemma
Corrected cyclic complex and every-page factorization for minus DS of dual affine Vermas
Theorem
Flatness and braid monodromy of the WZW KZ connection
Lemma
Exact principal minus reduction and vanishing of minimal-series extensions
Lemma
Actual principal W extension splitting gives semisimplicity in every specified admissible grading
Sources
- Finite semisimple Lie algebra and symmetric adjoint action
- Tomoyuki Arakawa, Two-sided BGG resolutions of admissible representations
- Pavel Etingof, Representations of Lie Groups
- Etingof, Frenkel, and Kirillov, Lectures on Representation Theory and KZ Equations
- Tsuchiya, Ueno, and Yamada, Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries
- Belavin, Polyakov, and Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory
- Paul Ginsparg, Applied Conformal Field Theory
- Creutzig, Jiang, Orosz Hunziker, Ridout, and Yang, Tensor Categories Arising from the Virasoro Algebra
- Tomoyuki Arakawa and Anne Moreau, Arc spaces and vertex algebras
- Pavel Etingof, Lie Groups and Lie Algebras II
- Wolfgang Soergel, Character formulas for tilting modules over Kac-Moody algebras
- Tomoyuki Arakawa, Rationality of W-algebras: principal nilpotent cases
- Ana Balibanu, Geometry of Semisimple Lie Algebras, Part I
- Beilinson and Drinfeld, Chiral Algebras, preliminary Chapter 4
- Tomoyuki Arakawa, Rationality of admissible affine vertex algebras in the category O
- Tomoyuki Arakawa, Introduction to W-algebras and their representation theory
- Tomoyuki Arakawa, Associated varieties of modules over Kac–Moody algebras and C2-cofiniteness of W-algebras
- Uhi Rinn Suh, Structure of classical affine and classical affine fractional W-algebras
- Tomoyuki Arakawa, Corrigendum to Rationality of admissible affine vertex algebras in the category O
- Tomoyuki Arakawa, Representation Theory of W-Algebras
- Tomoyuki Arakawa, Rationality of W-algebras, principal nilpotent cases
- Chongying Dong, Haisheng Li and Geoffrey Mason, Vertex operator algebras associated to admissible representations of affine sl2
- Alexander A. Voronov, Semi-infinite homological algebra
- Tomoyuki Arakawa, Vanishing of cohomology associated to quantized Drinfeld-Sokolov reduction