DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Highest-weight vector and module for Virasoro

Definition

Let $V$ be a representation of the Virasoro algebra Virasoro algebra in the L_m convention. A nonzero vector $v \in V$ is a highest-weight vector of weight $h \in C$ and central charge $c \in C$ if $L_{n} v = 0$ for every $n > 0$ , $L_{0} v = h v$ , and $C v = c v$ . The highest-weight module generated by $v$ is the submodule spanned by all finite words in the Virasoro generators applied to $v$ . This definition asserts neither irreducibility nor unitarity; quotienting the generated module by a proper submodule is an additional choice.

Depends on

Used by

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Dependency tree · two levels

7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Antony Wassermann, Kac–Moody and Virasoro Algebras, Chapter IV §1 (standard reference, not scraped)
Pavel Ginsparg, Applied Conformal Field Theory, §§3.1–3.3 (standard reference, not scraped)