Journal
INVENTIONES MATHEMATICAE
Volume 218, Issue 1, Pages 145-195Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-019-00884-3
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Funding
- JSPS KAKENHI [17H01086, 17K18724]
- NSERC [RES0019997]
- Simons Foundation [318755]
- Grants-in-Aid for Scientific Research [17K18724, 17H01086] Funding Source: KAKEN
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We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin's conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the discrete series of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Kazama-Suzuki coset vertex superalgebras is derived.
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