Home Publications Research Grants Inventions & Patents Awards Additional Research Activities Faculties & Institutions Research Areas

Orbifolds and Cosets of Minimal W -Algebras

Arakawa T, Creutzig T, Kawasetsu K, Linshaw AR (2017)

---

Publication Type: Journal article

Publication year: 2017

Journal

Book Volume: 355

Pages Range: 339-372

Journal Issue: 1

DOI: 10.1007/s00220-017-2901-2

Abstract

Let g be a simple, finite-dimensional Lie (super)algebra equipped with an embedding of sl2 inducing the minimal gradation on g. The corresponding minimal W-algebra W^k(g, e-θ) introduced by Kac and Wakimoto has strong generators in weights 1 , 2 , 3 / 2 , and all operator product expansions are known explicitly. The weight one subspace generates an affine vertex (super)algebra Vk′(g♮), where g^♮⊂ g denotes the centralizer of sl2. Therefore, W^k(g, e-θ) has an action of a connected Lie group G0♮ with Lie algebra g0♮, where g0♮ denotes the even part of g^♮. We show that for any reductive subgroup G⊂G0♮, and for any reductive Lie algebra g^′⊂ g^♮, the orbifold Ok=Wk(g,e-θ)G and the coset C^k= Com (V(g^′) , W^k(g, e-θ)) are strongly finitely generated for generic values of k. Here V(g^′) denotes the affine vertex algebra associated to g^′. We find explicit minimal strong generating sets for C^k when g^′= g^♮ and g is either sln, sp2n, sl(2 | n) for n≠ 2 , psl(2 | 2) , or osp(1 | 4). Finally, we conjecture some surprising coincidences among families of cosets Ck which are the simple quotients of C^k, and we prove several cases of our conjecture.

Involved external institutions

How to cite

APA:

Arakawa, T., Creutzig, T., Kawasetsu, K., & Linshaw, A.R. (2017). Orbifolds and Cosets of Minimal W -Algebras. Communications in Mathematical Physics, 355(1), 339-372. https://doi.org/10.1007/s00220-017-2901-2

MLA:

Arakawa, Tomoyuki, et al. "Orbifolds and Cosets of Minimal W -Algebras." Communications in Mathematical Physics 355.1 (2017): 339-372.

BibTeX: Download