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C2C_2-cofiniteness of logarithmic WW-algebras

Primarily AI-generated textHuman understanding: no partsmath.QA — Quantum Algebra

Contributed by Andrew Riesen ↗

Version 1 / Oct 15, 2026 / CC BY 4.0

Abstract

Let g\mathfrak{g} be a finite-dimensional simple complex Lie algebra with root lattice QQ and lacing number tt, equipped with an invariant bilinear form normalized so that long roots have squared length two. We prove C2C_2-cofiniteness of the Feigin--Tipunin logarithmic WW-algebra $\W_p(Q)$ for p=tm≥2p=tm\geq2 and $m\geq h^\vee_{{}^L\g}-1$, where $h^\vee_{{}^L\g}$ is the dual Coxeter number of the Langlands dual. Drinfeld--Sokolov reduction of induced affine Weyl modules gives graded generators for the multiplicity spaces of the conformal group action. Their degree bounds show that the intrinsic C2C_2-algebra is a finite module over the polynomial C2C_2-algebra of its principal invariant subalgebra. Adjoint contractions produce a finite relation ideal in this polynomial ring. Heisenberg normal ordering and a constant-coefficient differential equation show that its common zero is the origin. The argument gives explicit sufficient bounds and strong fin

Provenance statement

The high-level argument is understood by the author. The detailed proofs were generated primarily with AI assistance and have not yet been independently verified by a human. The author is currently reviewing these arguments and intends to prepare a revised, human-readable version following detailed mathematical verification.

References

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Version history

  1. v1Submitted by Andrew RiesenInitial depositCurrentOct 15, 2026