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Seminormal Representations of Weyl Groups and Iwahori‐Hecke Algebras
Author(s) -
Ram Arun
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000282
Subject(s) - mathematics , pure mathematics , weyl group , symmetric group , coxeter group , algebra over a field , hecke algebra , computation , irreducible representation , group (periodic table) , algorithm , chemistry , organic chemistry
The purpose of this paper is to describe a general procedure for computing analogues of Young's seminormal representations of the symmetric groups. The method is to generalize the Jucys‐Murphy elements in the group algebras of the symmetric groups to arbitrary Weyl groups and Iwahori‐Hecke algebras. The combinatorics of these elements allows one to compute irreducible representations explicitly and often very easily. In this paper we do these computations for Weyl groups and Iwahori‐Hecke algebras of types A n , B n , D n , G 2 . Although these computations are in reach for types F 4 , E 6 and E 7 , we shall postpone this to another work. 1991 Mathematics Subject Classification : primary 20F55, 20C15; secondary 20C30, 20G05.