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\n In all finite Coxeter types but\n \n \n \n \n \n I<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n 12<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n I_2(12)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n ,\n \n \n \n \n \n I<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n 18<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n I_2(18)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , and\n \n \n \n \n \n I<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n 30<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n I_2(30)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , we classify simple transitive\n \n \n \n 2<\/mml:mn>\n 2<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -representations for the quotient of the\n \n \n \n 2<\/mml:mn>\n 2<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -category of Soergel bimodules over the coinvariant algebra which is associated with the two-sided cell that is the closest one to the two-sided cell containing the identity element. It turns out that, in most of the cases, simple transitive\n \n \n \n 2<\/mml:mn>\n 2<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -representations are exhausted by cell\n \n \n \n 2<\/mml:mn>\n 2<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -representations. However, in Coxeter types\n \n \n \n \n \n I<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n (<\/mml:mo>\n 2<\/mml:mn>\n k<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n I_2(2k)<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , where\n \n \n \n \n k<\/mml:mi>\n \n \u2265\n \n <\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n k\\geq 3<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n , there exist simple transitive\n \n \n \n 2<\/mml:mn>\n 2<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -representations which are not equivalent to cell\n \n \n \n 2<\/mml:mn>\n 2<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -representations.\n <\/p>","DOI":"10.1090\/tran\/7456","type":"journal-article","created":{"date-parts":[[2017,11,15]],"date-time":"2017-11-15T11:09:22Z","timestamp":1510744162000},"page":"5551-5590","source":"Crossref","is-referenced-by-count":19,"special_numbering":"1011","title":["Simple transitive 2-representations of small quotients of Soergel bimodules"],"prefix":"10.1090","volume":"371","author":[{"given":"Tobias","family":"Kildetoft","sequence":"first","affiliation":[]},{"given":"Marco","family":"Mackaay","sequence":"additional","affiliation":[]},{"given":"Volodymyr","family":"Mazorchuk","sequence":"additional","affiliation":[]},{"given":"Jakob","family":"Zimmermann","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2018,8,8]]},"reference":[{"key":"1","isbn-type":"print","first-page":"1","article-title":"On crossed product rings with twisted involutions, their module categories and \ud835\udc3f-theory","author":"Bartels, Arthur","year":"2010","ISBN":"https:\/\/id.crossref.org\/isbn\/9781571461445"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s000290050047","article-title":"A categorification of the Temperley-Lieb algebra and Schur quotients of \ud835\udc48(\ud835\udd30\ud835\udd29\u2082) via projective and Zuckerman functors","volume":"5","author":"Bernstein, Joseph","year":"1999","journal-title":"Selecta Math. 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