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On the Induction of Kazhdan–Lusztig Cells
Author(s) -
Geck Meinolf
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002236
Subject(s) - mathematics , coxeter group , coxeter complex , pure mathematics , weyl group , coxeter element , artin group , mathematics subject classification , argument (complex analysis) , algebra over a field , biochemistry , chemistry
Barbasch and Vogan showed that the Kazhdan–Lusztig cells of a finite Weyl group are compatible with parabolic subgroups. Their proof uses the known bridge between the theory of cells and the theory of primitive ideals. In this paper, an elementary, self‐contained proof of this result is provided, which works for arbitrary Coxeter groups and Lusztig's general definition of cells (involving Iwahori–Hecke algebras with unequal parameters). The argument is based on a recent paper by Howlett and Yin. 2000 Mathematics Subject Classification 20C08.