{"id":509,"date":"2017-04-12T10:57:20","date_gmt":"2017-04-12T08:57:20","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=509"},"modified":"2017-04-12T11:01:40","modified_gmt":"2017-04-12T09:01:40","slug":"on-principal-realization-of-modules-for-the-affine-lie-algebra-a_11-at-the-critical-level","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/on-principal-realization-of-modules-for-the-affine-lie-algebra-a_11-at-the-critical-level\/","title":{"rendered":"On principal realization of modules for the affine Lie algebra \"A_1^{(1)}\" at the critical level"},"content":{"rendered":"

Abstract: We present complete realization of irreducible \"A_1^{(1)}\"-modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z-algebra approach to this construction. All irreducible highest weight \"A_1^{(1)}\"-modules at the critical level are realized on the vector space \"M_{\tfrac {1}{2}+\mathbb{Z}}(1)^{\otimes 2}\" \u00a0where \u00a0\"M_{\tfrac {1}{2} + \mathbb{Z}}(1)\"\u00a0is the polynomial ring \"{\mathbb{C}}[\alpha (-1/2), \alpha (-3/2),\dots ]\". Explicit combinatorial bases for these modules are also given.<\/p>\n

Authors:<\/span> Dra\u017een Adamovi\u0107<\/a>, Naihuan Jing<\/a> and Kailash C. Misra<\/a>
\nJournal:<\/span> Trans. Amer. Math. Soc. 369<\/strong> (2017), 5113-5136
\nMSC (2010):<\/span> Primary 17B69; Secondary 17B67, 17B68, 81R10
\nDOI:<\/span> https:\/\/doi.org\/10.1090\/tran\/7009
\nPublished electronically:<\/span> March 1, 2017<\/p>\n","protected":false},"excerpt":{"rendered":"

Abstract: We present complete realization of irreducible -modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z-algebra approach to this construction. All irreducible highest weight -modules at the […]<\/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\/wp-json\/wp\/v2\/posts\/509"}],"collection":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/comments?post=509"}],"version-history":[{"count":3,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/509\/revisions"}],"predecessor-version":[{"id":512,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/509\/revisions\/512"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=509"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}