Show simple item record C. A. en_US Thomas P. en_US 2009-11-17T13:48:22Z 2009-11-17T13:48:22Z 2008-02-01 en_US
dc.identifier en_US
dc.identifier.citation Pallikaros , C A & McDonough , T P 2008 , ' On subsequences and certain elements which determine various cells in S_n ' Journal of Algebra , vol 319 , no. 3 , pp. 1249-1263 . , 10.1016/j.jalgebra.2007.03.047 en_US
dc.identifier.other PURE: 142115 en_US
dc.identifier.other dspace: 2160/3533 en_US
dc.description.abstract We study the relation between certain increasing and decreasing subsequences occurring in the row form of certain elements in the symmetric group, following Schensted [C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961) 179–191] and Greene [C. Greene, An extension of Schensted's theorem, Adv. Math. 14 (1974) 254–265], and the Kazhdan–Lusztig cells [D.A. Kazhdan, G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979) 165–184] of the symmetric group to which they belong. We show that, in the two-sided cell corresponding to a partition λ, there is an explicitly defined element dλ, each of whose prefixes can be used to obtain a left cell by multiplying the cell containing the longest element of the parabolic subgroup associated with λ on the right. Furthermore, we show that the elements of these left cells are those which possess increasing and decreasing subsequences of certain types. The results in this paper lead to efficient algorithms for the explicit descriptions of many left cells inside a given two-sided cell, and the authors have implemented these algorithms in GAP. en_US
dc.format.extent 15 en_US
dc.relation.ispartof Journal of Algebra en_US
dc.subject Symmetric groups en_US
dc.subject Young tableaux en_US
dc.subject Kazhdan–Lusztig cells en_US
dc.subject Coxeter groups en_US
dc.title On subsequences and certain elements which determine various cells in S_n en_US
dc.contributor.pbl Aberystwyth University en_US
dc.contributor.pbl Algebraic Combinatorics en_US

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