{"id":697,"date":"2019-11-27T09:44:04","date_gmt":"2019-11-27T07:44:04","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=697"},"modified":"2019-11-27T09:44:04","modified_gmt":"2019-11-27T07:44:04","slug":"conformal-embeddings-in-affine-vertex-superalgebras","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/hr\/conformal-embeddings-in-affine-vertex-superalgebras\/","title":{"rendered":"Conformal embeddings in affine vertex superalgebras"},"content":{"rendered":"

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Authors:\u00a0Dra\u017een Adamovi\u0107,\u00a0Pierluigi M\u00f6seneder Frajria,\u00a0Paolo Papi,\u00a0Ozren Per\u0161e<\/strong><\/p>\n

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Advances in Mathematics,\u00a0Volume 360,\u00a022 January 2020, 106918<\/p>\n

https:\/\/doi.org\/10.1016\/j.aim.2019.106918<\/a><\/p>\n<\/div>\n

Abstract:<\/strong>\u00a0This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras\u00a0[6]<\/a>,\u00a0[7]<\/a>,\u00a0[8]<\/a>. Here we consider conformal embeddings in simple affine vertex superalgebra\u00a0\"V_k(\mathfrak{g})\"\u00a0<\/span><\/span><\/span><\/span><\/span>where\u00a0\"\mathfrak{g}=\mathfrak{g}_{\bar{0}} \oplus \mathfrak{g}_{\bar{1}}\"\u00a0<\/span><\/span><\/span>is a basic classical simple Lie superalgebra. Let\u00a0\"\mathcal{V}_k(\mathfrak{g}_{\bar{0}})\"\u00a0<\/span><\/span><\/span><\/span><\/span>be the subalgebra of\u00a0\"V_k(\mathfrak{g})\"<\/span><\/span><\/span><\/span><\/span>\u00a0generated by\u00a0\"\mathfrak{g}_{\bar{0}}\". We first classify all levels\u00a0\"k\"\u00a0for which the embedding\u00a0\"\mathcal{V}_k(\mathfrak{g}_{\bar{0}})\"\u00a0in\u00a0\"V_k(\mathfrak{g})\"\u00a0is conformal. Next we prove that, for a large family of such conformal levels,\u00a0\"V_k(\mathfrak{g})\"\u00a0is a completely reducible\"\mathcal{V}_k(\mathfrak{g}_{\bar{0}})\"\u2013module and obtain decomposition rules. Proofs are based on fusion rules arguments and on the representation theory of certain affine vertex algebras. The most interesting case is the decomposition of\u00a0\"V_{-2}(osp(2n+8|2n))\"<\/span><\/span><\/span><\/span><\/span>\u00a0as a finite, non simple current extension of\u00a0\"V_{-2}(D_{n+4})\otimes V_1(C_n)\". This decomposition uses our previous work\u00a0[10]<\/a>\u00a0on the representation theory of\u00a0\"V_{-2}(D_{n+4})\".<\/p>\n

We also study conformal embeddings\u00a0\"gl(n|m)↪ \hookrightarrow sl(n+1|m)\"\u00a0<\/span>and in most cases we obtain decomposition rules.<\/p>\n

<\/p>","protected":false},"excerpt":{"rendered":"

Authors:\u00a0Dra\u017een Adamovi\u0107,\u00a0Pierluigi M\u00f6seneder Frajria,\u00a0Paolo Papi,\u00a0Ozren Per\u0161e Advances in Mathematics,\u00a0Volume 360,\u00a022 January 2020, 106918 https:\/\/doi.org\/10.1016\/j.aim.2019.106918 Abstract:\u00a0This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras\u00a0[6],\u00a0[7],\u00a0[8]. Here we consider conformal embeddings in simple affine vertex superalgebra\u00a0\u00a0where\u00a0\u00a0is a basic classical simple Lie superalgebra. Let\u00a0\u00a0be the subalgebra of\u00a0\u00a0generated […]<\/a><\/p>\n<\/div>","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[18,14],"tags":[],"_links":{"self":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/697"}],"collection":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/comments?post=697"}],"version-history":[{"count":10,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/697\/revisions"}],"predecessor-version":[{"id":707,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/697\/revisions\/707"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/media?parent=697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/categories?post=697"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/tags?post=697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}