Kazhdan and Lusztig have shown how to partition a Coxeter group into cells. In this paper, we use the theory of Vogan classes to obtain a first characterisation of the left cells of type with respect to a certain choice of weight function.
Revised : 2019-03-06
Accepted : 2019-03-14
Published online : 2019-12-04
DOI : https://doi.org/10.5802/alco.74
Keywords: Coxeter groups, Iwahori–Hecke algebras, Kazhdan–Lusztig cells
@article{ALCO_2019__2_6_1033_0,
author = {Howse, Edmund},
title = {Vogan classes in type $B\_n$},
journal = {Algebraic Combinatorics},
publisher = {MathOA foundation},
volume = {2},
number = {6},
year = {2019},
pages = {1033-1057},
doi = {10.5802/alco.74},
language = {en},
url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1033_0}
}
Howse, Edmund. Vogan classes in type $B_n$. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1033-1057. doi : 10.5802/alco.74. alco.centre-mersenne.org/item/ALCO_2019__2_6_1033_0/
[1] Robinson–Schensted correspondence and left cells, Combinatorial methods in representation theory (Kyoto, 1998) (Adv. Stud. Pure Math.) Volume 28, Kinokuniya, Tokyo, 2000, pp. 1-20 | MR 1855588 (2002i:20003) | Zbl 0986.05097
[2] Two-sided cells in type (asymptotic case), J. Algebra, Volume 304 (2006) no. 1, pp. 216-236 | Article | MR 2255826 (2007j:20003) | Zbl 1150.20004
[3] Semicontinuity properties of Kazhdan–Lusztig cells, New Zealand J. Math., Volume 39 (2009), pp. 171-192 | MR 2772408 (2012b:20005) | Zbl 1231.20004
[4] On Kazhdan–Lusztig cells in type , J. Algebraic Combin., Volume 31 (2010) no. 1, pp. 53-82 | Article | MR 2577478 (2011b:20014) | Zbl 1198.20034
[5] Erratum to: On Kazhdan–Lusztig cells in type , J. Algebraic Combin., Volume 35 (2012) no. 3, pp. 515-517 | Article | MR 2892987 | Zbl 1376.20039
[6] Hecke algebras with unequal parameters and Vogan’s left cell invariants, Representations of reductive groups (Prog. Math.) Volume 312, Birkhäuser/Springer, Cham, 2015, pp. 173-187 | Article | MR 3495796 | Zbl 1343.20004
[7] On domino insertion and Kazhdan–Lusztig cells in type , Representation theory of algebraic groups and quantum groups (Progr. Math.) Volume 284, Birkhäuser/Springer, New York, 2010, pp. 33-54 | Article | MR 2761947 (2011k:20004) | Zbl 1223.20003
[8] Left cells in type with unequal parameters, Represent. Theory, Volume 7 (2003), pp. 587-609 | Article | MR 2017068 (2004j:20007) | Zbl 1070.20004
[9] On the classification of primitive ideals for complex classical Lie algebras. I, Compositio Math., Volume 75 (1990) no. 2, pp. 135-169 | MR 1065203 (91m:17011) | Zbl 0737.17003
[10] On the classification of primitive ideals for complex classical Lie algebra. II, Compositio Math., Volume 81 (1992) no. 3, pp. 307-336 | MR 1149172 (93g:17018) | Zbl 0762.17007
[11] On the classification of primitive ideals for complex classical Lie algebras. III, Compositio Math., Volume 88 (1993) no. 2, pp. 187-234 | MR 1237920 (94i:17017) | Zbl 0798.17007
[12] On the induction of Kazhdan–Lusztig cells, Bull. London Math. Soc., Volume 35 (2003) no. 5, pp. 608-614 | Article | MR 1989489 (2004d:20003) | Zbl 1045.20004
[13] Computing Kazhdan–Lusztig cells for unequal parameters, J. Algebra, Volume 281 (2004) no. 1, pp. 342-365 | Article | MR 2091976 (2005g:20007) | Zbl 1064.20006
[14] Relative Kazhdan–Lusztig cells, Represent. Theory, Volume 10 (2006), p. 481-524) | Article | MR 2266700 (2007i:20011) | Zbl 1139.20003
[15] : computing with (finite) Coxeter groups and Iwahori–Hecke algebras, LMS J. Comput. Math., Volume 15 (2012), pp. 231-256 | Article | MR 2988815 | Zbl 1296.20009
[16] Characters of finite Coxeter groups and Iwahori–Hecke algebras, London Mathematical Society Monographs. New Series, Volume 21, The Clarendon Press, Oxford University Press, New York, 2000, xvi+446 pages | MR 1778802 (2002k:20017) | Zbl 0996.20004
[17] Einhüllende Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Volume 3, Springer-Verlag, Berlin, 1983, ii+298 pages | Article | MR 721170 | Zbl 0541.17001
[18] Representations of Coxeter groups and Hecke algebras, Invent. Math., Volume 53 (1979) no. 2, pp. 165-184 | Article | MR 560412 (81j:20066) | Zbl 0499.20035
[19] The art of computer programming. Volume 3, Addison–Wesley Publishing Co., Reading, Mass.–London–Don Mills, Ont., 1973, xi+722 pp. (1 foldout) pages (Sorting and searching, Addison–Wesley Series in Computer Science and Information Processing) | MR 0445948 (56 #4281) | Zbl 0302.68010
[20] Left cells in Weyl groups, Lie group representations, I (College Park, Md., 1982/1983) (Lecture Notes in Math.) Volume 1024, Springer, Berlin, 1983, pp. 99-111 | Article | MR 727851 (85f:20035) | Zbl 0537.20019
[21] Hecke algebras with unequal parameters, CRM Monograph Series, Volume 18, American Mathematical Society, Providence, RI, 2003, vi+136 pages | MR 1974442 (2004k:20011) | Zbl 1051.20003
[22] Hecke algebras with unequal parameters (2014) (http://arxiv.org/pdf/math/0208154.pdf) | Zbl 1051.20003
[23] Knuth relations for the hyperoctahedral groups, J. Algebraic Combin., Volume 29 (2009) no. 4, pp. 509-535 | Article | MR 2506719 | Zbl 1226.05261
[24] Longest increasing and decreasing subsequences, Canad. J. Math., Volume 13 (1961), pp. 179-191 | Article | MR 0121305 (22 #12047) | Zbl 0097.25202
[25] A generalized -invariant for the primitive spectrum of a semisimple Lie algebra, Math. Ann., Volume 242 (1979) no. 3, pp. 209-224 | Article | MR 545215 (81e:17014) | Zbl 0387.17007
