Universal Dual-Coset Virasoro Law
Abstract
Universal Dual-Coset Virasoro Law
For every finite rank and all integer m,n, both original inverse-Gram equations imply [moduleL_m,moduleL_n]=(m-n)moduleL_(m+n)+delta(m+n,0) rank(D)(m^3-m)/12 times identity. No rational shift, positive Gram or auxiliary inverse is required. The accepted original Virasoro, current and Heisenberg laws are used. The current correction contributes m u^T G u at m+n=0; since m-n=2m, the constant half-norm shift is exactly absorbed into moduleL_0.
Classical construction context: Bakalov-Kac, math/0402315v1, section 4.1. The imported Sugawara architecture retains Kalle Kytola’s Apache-2.0 attribution and VirasoroProject revision 5ff4245383b2cdd4eea7a0524bc1274c32041eb4. The finite reductions and actual-action connections are native mathematical proofs; no external novelty is asserted.
Theorem 1.1 (moduleL virasoro).
Lean statement: D5/S3/VertexAlgebra/Sectors/LatticeDualCosetVirasoroLaw.moduleL_virasoro
Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/Sectors/LatticeDualCosetVirasoroLaw.moduleL_virasoro (✓ std3). ∎
Source. Repository-derived.
Commentary.
All integer actual original-omega modes obey Virasoro with central charge rank(D), including rank zero, under the two original inverse equations alone.