Minimal determining sets for certain $W$-graph ideals

نویسندگان
McDonough, Thomas P. ID 1
Pallikaros, Christos A. ID 2

1 Department of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ, United Kingdom

2 Department of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, 1678 Nicosia, Cyprus

doi
10.22108/ijgt.2022.131838.1764
چکیده

We consider Kazhdan-Lusztig cells of the symmetric group $S_n$ containing the longest element of a standard parabolic subgroup of $S_n$. Extending some of the ideas in [Beiträge zur Algebra und Geometrie, 59 (2018) no.~3 523--547] and [Journal of Algebra and Its Applications, 20 (2021) no.~10 2150181], we determine the rim of some additional families of cells and also of certain induced unions of cells. These rims provide minimal determining sets for certain $W$-graph ideals introduced in [Journal of Algebra, 361 (2012) 188--212].

کلیدواژه‌ها
$W$-graph ideal, Kazhdan-Lusztig cell, reduced form