Trialities of $\mathcal{W}$-algebras
نویسندگان
چکیده
We prove the conjecture of Gaiotto and Rap\v{c}\'ak that $Y$-algebras $Y_{L,M,N}[\psi]$ with one parameters $L,M,N$ zero, are simple one-parameter quotients universal two-parameter $\mathcal{W}_{1+\infty}$-algebra, satisfy a symmetry known as triality. These defined cosets certain non-principal $\mathcal{W}$-algebras $\mathcal{W}$-superalgebras by their affine vertex subalgebras, triality is an isomorphism between three such algebras. Special cases our result provide new unified proofs many theorems open conjectures in literature on type $A$. This includes (1) Feigin-Frenkel duality, (2) coset realization principal due to Arakawa us, (3) Feigin Semikhatov's conjectured subregular $\mathcal{W}$-algebras, $\mathcal{W}$-superalgebras, superalgebras, (4) rationality van Ekeren, (5) identification Heisenberg rational was physics over 25 years ago. Finally, we Proch\'azka explicit truncation curves realizing $\mathcal{W}_{1+\infty}$-quotients, minimal strong generating types.
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ژورنال
عنوان ژورنال: Cambridge journal of mathematics
سال: 2022
ISSN: ['2168-0930', '2168-0949']
DOI: https://doi.org/10.4310/cjm.2022.v10.n1.a2