{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T14:35:31Z","timestamp":1649082931477},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> Kudryavtseva and Mazorchuk exhibited Schur\u2013Weyl duality between the rook monoid algebra [Formula: see text] and the subalgebra [Formula: see text] of the partition algebra [Formula: see text] acting on [Formula: see text]. In this paper, we consider a subalgebra [Formula: see text] of [Formula: see text] such that there is Schur\u2013Weyl duality between the actions of [Formula: see text] and [Formula: see text] on [Formula: see text]. This paper studies the representation theory of partition algebras [Formula: see text] and [Formula: see text] for rook monoids inductively by considering the multiplicity free tower [Formula: see text] Furthermore, this inductive approach is established as a spectral approach by describing the Jucys\u2013Murphy elements and their actions on the canonical Gelfand\u2013Tsetlin bases, determined by the aforementioned multiplicity free tower, of irreducible representations of [Formula: see text] and [Formula: see text]. Also, we describe the Jucys\u2013Murphy elements of [Formula: see text] which play a central role in the demonstration of the actions of Jucys\u2013Murphy elements of [Formula: see text] and [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196721500399","type":"journal-article","created":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T02:14:46Z","timestamp":1622859286000},"page":"831-864","source":"Crossref","is-referenced-by-count":0,"title":["Jucys\u2013Murphy elements of partition algebras for the rook monoid"],"prefix":"10.1142","volume":"31","author":[{"given":"Ashish","family":"Mishra","sequence":"first","affiliation":[{"name":"Faculdade de Matem\u00e1tica, Instituto de Ci\u00eancias Exatas e Naturais, Universidade Federal do Par\u00e1, Rua Augusto Corr\u00eaa, 01-Guam\u00e1, Bel\u00e9m 66075-110, Par\u00e1, Brazil"}]},{"given":"Shraddha","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Uppsala University, Box. 480, SE-75106, Uppsala, Sweden"}]}],"member":"219","published-online":{"date-parts":[[2021,6,3]]},"reference":[{"key":"S0218196721500399BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-05141-9_1"},{"key":"S0218196721500399BIB002","doi-asserted-by":"publisher","DOI":"10.1112\/jlms.12175"},{"key":"S0218196721500399BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-017-0748-4"},{"key":"S0218196721500399BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196708004470"},{"key":"S0218196721500399BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.04.027"},{"key":"S0218196721500399BIB006","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700039227"},{"key":"S0218196721500399BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0979-9"},{"issue":"1","key":"S0218196721500399BIB008","first-page":"10","volume":"9","author":"Grood C.","year":"2002","journal-title":"Electron. 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