{"id":612,"date":"2018-09-30T15:44:34","date_gmt":"2018-09-30T13:44:34","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=612"},"modified":"2018-10-08T13:28:48","modified_gmt":"2018-10-08T11:28:48","slug":"singular-bgg-complexes-over-isotropic-2-grassmannian","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/singular-bgg-complexes-over-isotropic-2-grassmannian\/","title":{"rendered":"Singular BGG Complexes Over Isotropic 2-Grassmannian"},"content":{"rendered":"

Authors: Denis Husad\u017ei\u0107, Rafael Mr\u0111en<\/strong><\/p>\n

Journal of Lie Theory 28 (2018), No. 4, 1149–1164<\/b><\/p>\n

http:\/\/www.heldermann.de\/JLT\/JLT28\/JLT284\/jlt28054.htm<\/a><\/p>\n

(preprint:\u00a0https:\/\/arxiv.org\/abs\/1803.10497<\/a>)<\/p>\n

Abstract:\u00a0<\/strong>We construct exact sequences of invariant differential operators acting on sections of certain homogeneous vector bundles in singular infinitesimal character, over the isotropic\u00a02<\/span><\/span><\/span><\/span>-Grassmannian. This space is equal to\u00a0G<\/span>\/<\/span><\/span><\/span>P<\/span><\/span><\/span><\/span>, where\u00a0G<\/span><\/span><\/span><\/span>\u00a0is\u00a0Sp<\/span><\/span>(<\/span>2<\/span>n<\/span>,<\/span>C<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>, and\u00a0P<\/span><\/span><\/span><\/span>\u00a0its standard parabolic subgroup having the Levi factor\u00a0GL<\/span><\/span>(<\/span>2<\/span>,<\/span>C<\/span><\/span><\/span>)<\/span>\u00d7<\/span>Sp<\/span><\/span>(<\/span>2<\/span>n<\/span>\u2212<\/span>4<\/span>,<\/span>C<\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>. The constructed sequences are analogues of the Bernstein-Gelfand-Gelfand resolutions. We do this by considering the Penrose transform over an appropriate double fibration. The result differs from the Hermitian situation.<\/p>\n

Keywords:<\/strong>\u00a0Bernstein-Gelfand-Gelfand (BGG) complexes, singular infinitesimal character, isotropic 2-Grassmannian, invariant differential operators, Penrose transform.<\/p>\n

MSC:<\/strong>\u00a058J10; 53C28, 53A55.<\/p>\n","protected":false},"excerpt":{"rendered":"

Authors: Denis Husad\u017ei\u0107, Rafael Mr\u0111en Journal of Lie Theory 28 (2018), No. 4, 1149–1164 http:\/\/www.heldermann.de\/JLT\/JLT28\/JLT284\/jlt28054.htm (preprint:\u00a0https:\/\/arxiv.org\/abs\/1803.10497) Abstract:\u00a0We construct exact sequences of invariant differential operators acting on sections of certain homogeneous vector bundles in singular infinitesimal character, over the isotropic\u00a02-Grassmannian. This space is equal to\u00a0G\/P, where\u00a0G\u00a0is\u00a0Sp(2n,C), and\u00a0P\u00a0its standard parabolic subgroup having […]<\/a><\/p>\n<\/div>","protected":false},"author":5,"featured_media":622,"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\/612"}],"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=612"}],"version-history":[{"count":3,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/612\/revisions"}],"predecessor-version":[{"id":615,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/612\/revisions\/615"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media\/622"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=612"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}