COSETS FROM EQUIVARIANT W-ALGEBRAS

Article Mathematics

Gluing vertex algebras

Thomas Creutzig et al.

Summary: In this study, the relationship between commutative algebras in braided tensor categories and braid-reversed tensor equivalences is explored, based on the representation theory of vertex algebras. By providing a detailed account of canonical algebra construction in the Deligne product, it is shown that under certain conditions, braid-reversed equivalences exist in specific simple algebraic structures.

ADVANCES IN MATHEMATICS (2022)

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Article Physics, Mathematical

On semisimplicity of module categories for finite non-zero index vertex operator subalgebras

Robert McRae

Summary: This article discusses the relationship between vertex operator algebras and the category of grading-restricted generalized modules, and gives conditions under which the category inherits semisimplicity from the A-module category. Furthermore, these results are generalized to the case of vertex operator superalgebras.

LETTERS IN MATHEMATICAL PHYSICS (2022)

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Article Mathematics, Applied

Quantum coordinate ring in WZW model and affine vertex algebra extensions

Yuto Moriwaki

Summary: This paper constructs various simple vertex superalgebras by using abelian cocycle twists of representation categories of quantum groups, solving the Creutzig and Gaiotto conjectures in the case of type ABC.

SELECTA MATHEMATICA-NEW SERIES (2022)

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Article Mathematics

Trialities of orthosymplectic W-algebras

Thomas Creutzig et al.

Summary: This paper proves the trialities among eight families of W-(super)algebras of types B, C, and D and provides a new interpretation of coset realizations. In terms of specific applications, the rationality of various vertex superalgebras and principal W-algebras is established.

ADVANCES IN MATHEMATICS (2022)

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Article Mathematics, Applied

Urod algebras and Translation of W-algebras

Tomoyuki Arakawa et al.

Summary: This work introduces Urod algebras associated with simply laced Lie algebras and the concept of translation of W-algebras. The key results are derived by showing the commutation between quantum Hamiltonian reduction and tensoring with integrable representations. The work also presents new constructions of automorphisms of vertex algebras, which have independent interest. The applications of this work include fusion categories of modules of exceptional W-algebras and the construction of corner vertex algebras. The representation theoretic interpretation of the Nakajima-Yoshioka blowup equations for the moduli space of framed torsion free sheaves on CP2 is one of the major motivations.

FORUM OF MATHEMATICS SIGMA (2022)

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Article Mathematics

Duality of subregular W-algebras and principal W-superalgebras

Thomas Creutzig et al.

Summary: This paper proves Feigin-Frenkel type dualities between subregular W-algebras of type A and principal W-superalgebras of type B, as well as between the principal W-superalgebras of types sl(1 | n) and osp(2 | 2n). The results include isomorphisms of Heisenberg cosets at dual levels, and a novel Kazama-Suzuki type coset construction. Additionally, it is shown that the simple principal W-superalgebra and its Heisenberg coset are rational and/or C-2-cofinite under certain conditions.

ADVANCES IN MATHEMATICS (2021)

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Article Physics, Mathematical