Realizations of simple affine vertex algebras and their modules: the cases \({\widehat{sl(2)}}\) and \({\widehat{osp(1,2)}}\)

DOI10.1007/S00220-019-03328-4zbMATH Open1452.17027arXiv1711.11342OpenAlexW3010778776MaRDI QIDQ1736250

Author name not available (Why is that?)

Publication date: 26 March 2019

Published in: (Search for Journal in Brave)

Abstract: We study embeddings of the simple admissible affine vertex algebras

V_{k} (s l (2))

and

V_{k} (o s p (1, 2))

,

k o t i n {B b b Z}_{g e 0}

, into the tensor product of rational Virasoro and

N = 1

Neveu-Schwarz vertex algebra with lattice vertex algebras. We prove that the admissible affine vertex algebra

V_{k} (s l (2))

can be embedded into vertex algebra

L^{V i r} (c_{p, p^{'}}, 0) o t i m e s P i (0)

where

L^{V i r} (c_{p, p^{'}}, 0)

is suitable minimal Virasoro vertex algebra and

P i (0)

is a vertex algebra of lattice type. By using these realizations we construct a family of weight, logarithmic and Whittaker

w i d e h a t s l (2)

and

w i d e h a t o s p (1, 2)

--modules. As an application, we construct all irreducible degenerate Whittaker modules for

V_{k} (s l (2))

.

Full work available at URL: https://arxiv.org/abs/1711.11342

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