{"id":720,"date":"2020-05-20T20:01:53","date_gmt":"2020-05-20T18:01:53","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=720"},"modified":"2020-05-20T20:01:53","modified_gmt":"2020-05-20T18:01:53","slug":"bgg-complexes-in-singular-blocks-of-category-o","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/bgg-complexes-in-singular-blocks-of-category-o\/","title":{"rendered":"BGG complexes in singular blocks of category O"},"content":{"rendered":"

Authors:<\/strong>\u00a0Volodymyr Mazorchuk, Rafael Mr\u0111en<\/p>\n

Journal of Pure and Applied Algebra\u00a0224 (2020), Issue 12, 106449<\/p>\n

https:\/\/doi.org\/10.1016\/j.jpaa.2020.106449<\/a><\/p>\n

Abstract:\u00a0<\/strong>Using translation from the regular block, we construct and analyze properties of BGG complexes in singular blocks of BGG category\u00a0\"\mathcal{O}\"<\/span><\/span><\/span><\/span><\/span>. We provide criteria, in terms of the Kazhdan-Lusztig-Vogan polynomials, for such complexes to be exact. In the Koszul dual picture, exactness of BGG complexes is expressed as a certain condition on a generalized Verma flag of an indecomposable projective object in the corresponding block of parabolic category\u00a0\"\mathcal{O}\".<\/p>\n

In the second part of the paper, we construct BGG complexes in a more general setting of balanced quasi-hereditary algebras and show how our results for singular blocks can be used to construct BGG resolutions of simple modules in \"\mathcal{S}\"-subcategories in \"\mathcal{O}\".<\/p>\n","protected":false},"excerpt":{"rendered":"

Authors:\u00a0Volodymyr Mazorchuk, Rafael Mr\u0111en Journal of Pure and Applied Algebra\u00a0224 (2020), Issue 12, 106449 https:\/\/doi.org\/10.1016\/j.jpaa.2020.106449 Abstract:\u00a0Using translation from the regular block, we construct and analyze properties of BGG complexes in singular blocks of BGG category\u00a0. We provide criteria, in terms of the Kazhdan-Lusztig-Vogan polynomials, for such complexes to be exact. […]<\/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\/720"}],"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=720"}],"version-history":[{"count":2,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/720\/revisions"}],"predecessor-version":[{"id":722,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/posts\/720\/revisions\/722"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/media?parent=720"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/categories?post=720"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/wp-json\/wp\/v2\/tags?post=720"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}