{"id":589,"date":"2018-02-20T11:55:27","date_gmt":"2018-02-20T09:55:27","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=589"},"modified":"2018-02-20T11:55:27","modified_gmt":"2018-02-20T09:55:27","slug":"on-the-classification-of-non-equal-rank-affine-conformal-embeddings-and-applications","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/hr\/on-the-classification-of-non-equal-rank-affine-conformal-embeddings-and-applications\/","title":{"rendered":"On the classification of non-equal rank affine conformal embeddings and applications"},"content":{"rendered":"

Authors:\u00a0<\/span>Dra\u017een Adamovi\u0107, Victor G. Kac, Pierluigi M\u00f6seneder Frajria, Paolo Papi, Ozren Per\u0161e<\/p>\n

Selecta Mathematica<\/a>,\u00a0<\/span>pp 1\u201344<\/span><\/p>\n

https:\/\/doi.org\/10.1007\/s00029-017-0386-7<\/a><\/p>\n

Abstract: We complete the classification of conformal embeddings of a maximally reductive subalgebra\u00a0\"\mathfrak{k}\"<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00a0a simple Lie algebra\u00a0\"\mathfrak{g}\"\u00a0at non-integrable non-critical levels\u00a0k<\/em>\u00a0by dealing with the case when\u00a0\"\mathfrak{k}\"\u00a0has rank less than that of\u00a0\"\mathfrak{g}\". We describe some remarkable instances of decomposition of the vertex algebra\u00a0\"V_k(\"\\mathfrak{k}\")\"<\/span><\/span><\/span><\/span><\/span><\/span>\u00a0as a module for the vertex subalgebra generated by\u00a0\"\mathfrak{k}\". We discuss decompositions of conformal embeddings and constructions of new affine Howe dual pairs at negative levels. In particular, we study an example of conformal embeddings\u00a0\"A_1 \times A_1 \hookrightarrow C_3\"\u00a0at level \"k = -1/2\", and obtain explicit branching rules by applying certain\u00a0q<\/em>-series identity. In the analysis of conformal embedding\u00a0\"A_1 \times D_4 \hookrightarrow C_8\"\u00a0at level\u00a0\u00a0\u00a0\"k = -1/2\" we detect subsingular vectors which do not appear in the branching rules of the classical Howe dual pairs.<\/p>\n

Keywords: Conformal embedding Vertex operator algebra Non-equal rank subalgebra Howe dual pairs q-series identity<\/p>\n

Mathematics Subject Classification: Primary 17B69, Secondary 17B20 17B65<\/p>","protected":false},"excerpt":{"rendered":"

Authors:\u00a0Dra\u017een Adamovi\u0107, Victor G. Kac, Pierluigi M\u00f6seneder Frajria, Paolo Papi, Ozren Per\u0161e Selecta Mathematica,\u00a0pp 1\u201344 https:\/\/doi.org\/10.1007\/s00029-017-0386-7 Abstract: We complete the classification of conformal embeddings of a maximally reductive subalgebra\u00a0\u00a0a simple Lie algebra\u00a0\u00a0at non-integrable non-critical levels\u00a0k\u00a0by dealing with the case when\u00a0\u00a0has rank less than that of\u00a0. We describe some remarkable instances […]<\/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\/589"}],"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=589"}],"version-history":[{"count":6,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/589\/revisions"}],"predecessor-version":[{"id":596,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/589\/revisions\/596"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/media?parent=589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/categories?post=589"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/tags?post=589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}