Naslov
On parafermion vertex algebras of 𝔰𝔩(2) and 𝔰𝔩(3) at level -3/2

Autori
Adamović, Dražen ; Milas, Antun ; Wang, Qing

Izvornik
Communications in contemporary mathematics (0219-1997) 24 (2022), 1; 20500868, 20

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Vertex algebra ; W-algebra ; parafermion algebra

Sažetak
We study parafermion vertex algebras 𝑁_{; ; ; ; ; ; ; ; ; -3/2}; ; ; ; ; ; ; ; ; (𝔰𝔩(2)) and 𝑁_{; ; ; ; ; ; ; ; ; -3/2}; ; ; ; ; ; ; ; ; (𝔰𝔩(3)). Using the isomorphism between 𝑁−3/2(𝔰𝔩(3)) and the logarithmic vertex algebra W(2)_{; ; ; ; ; ; ; ; ; A_2}; ; ; ; ; ; ; ; ; ^0 from [D. Adamović, A realization of certain modules for the 𝑁=4 superconformal algebra and the affine Lie algebra 𝐴(1)2, Transform. Groups21(2) (2016) 299- 327], we show that these parafermion vertex algebras are infinite direct sums of irreducible modules for the Zamolodchikov algebra 𝒲(2, 3) of central charge 𝑐=−10, and that 𝑁−3/2(𝔰𝔩(3)) is a direct sum of irreducible 𝑁_{; ; ; ; ; ; ; ; ; -3/2}; ; ; ; ; ; ; ; ; (𝔰𝔩(2))- modules. As a byproduct, we prove certain conjectures about the vertex algebra W(2)_{; ; ; ; ; ; ; ; ; A_2}; ; ; ; ; ; ; ; ; ^0. We also obtain a vertex-algebraic proof of the irreducibility of a family of 𝒲(2, 3)_𝑐 modules at 𝑐=−10.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
University at Albany, SAD ; Xiamen University, Kina

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