{"id":597,"date":"2018-04-02T23:52:58","date_gmt":"2018-04-02T21:52:58","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=597"},"modified":"2018-04-02T23:52:58","modified_gmt":"2018-04-02T21:52:58","slug":"self-dual-and-logarithmic-representations-of-the-twisted-heisenberg-virasoro-algebra-at-level-zero","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/self-dual-and-logarithmic-representations-of-the-twisted-heisenberg-virasoro-algebra-at-level-zero\/","title":{"rendered":"Self-dual and logarithmic representations of the twisted Heisenberg\u2013Virasoro algebra at level zero"},"content":{"rendered":"

<\/p>\n

Dra\u017een Adamovi\u0107<\/span>\u00a0and\u00a0Gordan Radobolja<\/span>,\u00a0Commun. Contemp. Math.<\/i>
\nhttps:\/\/doi.org\/10.1142\/S0219199718500086<\/a><\/p>\n

\n
\n

This paper is a continuation of\u00a0[D. Adamovi\u0107 and G. Radobolja, Free field realization of the twisted Heisenberg\u2013Virasoro algebra at level zero and its applications,\u00a0J. Pure Appl. Algebra<\/i>\u00a0219<\/b>(10) (2015) 4322\u20134342]. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg\u2013Virasoro algebra \"\mathcal H\"\u00a0at level zero. We find explicit formulas for singular vectors in certain Verma modules. A free field realization of self-dual modules for \"\mathcal H\"\u00a0is presented by combining a bosonic construction of Whittaker modules from\u00a0[D. Adamovi\u0107, R. Lu and K. Zhao, Whittaker modules for the affine Lie algebra \"A_1^{(1)}\",\u00a0Adv. Math.<\/i>\u00a0289<\/b>\u00a0(2016) 438\u2013479,\u00a0arXiv:1409.5354<\/a>] with a construction of logarithmic modules for vertex algebras. As an application, we prove that there exists a non-split self-extension of irreducible self-dual module which is a logarithmic module of rank two. We construct a large family of logarithmic modules containing different types of highest weight modules as subquotients. We believe that these logarithmic modules are related with projective covers of irreducible modules in a suitable category of \"\mathcal H\"-modules.<\/p>\n<\/div>\n<\/div>\n

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Keywords:\u00a0<\/b>Heisenberg\u2013Virasoro algebra; logarithmic representations; Whittaker modules; self-dual modules; singular vectors<\/div>\n<\/div>\n
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AMSC:\u00a0<\/b>17B69, 17B67, 17B68, 81R10<\/div>\n<\/div>\n

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

Dra\u017een Adamovi\u0107\u00a0and\u00a0Gordan Radobolja,\u00a0Commun. Contemp. Math. https:\/\/doi.org\/10.1142\/S0219199718500086 This paper is a continuation of\u00a0[D. Adamovi\u0107 and G. Radobolja, Free field realization of the twisted Heisenberg\u2013Virasoro algebra at level zero and its applications,\u00a0J. Pure Appl. Algebra\u00a0219(10) (2015) 4322\u20134342]. We present certain new applications and generalizations of the free field realization of the twisted […]<\/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\/597"}],"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=597"}],"version-history":[{"count":2,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/597\/revisions"}],"predecessor-version":[{"id":600,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/597\/revisions\/600"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=597"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}