Universal two-parameter

نویسندگان

چکیده

We prove the longstanding physics conjecture that there exists a unique two-parameter ${\mathcal {W}}_{\infty }$ -algebra which is freely generated of type {W}}(2,3,\ldots )$ , and by weights $2$ $3$ fields. Subject to some mild constraints, all vertex algebras N)$ for $N$ can be obtained as quotients this universal algebra. As an application, we show $n\geq 3$ structure constants principal {W}}$ -algebras {W}}^k({\mathfrak s}{\mathfrak l}_n, f_{\text {prin}})$ are rational functions $k$ $n$ classify coincidences among simple {W}}_k({\mathfrak 2$ . also obtain many new between other arise cosets affine or nonprincipal -algebras.

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ژورنال

عنوان ژورنال: Compositio Mathematica

سال: 2021

ISSN: ['0010-437X', '1570-5846']

DOI: https://doi.org/10.1112/s0010437x20007514