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Dear Mrs. and Mr. Forum,

A new version of the Weyl-package is available on "samson.math.rwth-aachen.de"

(and hopefully soon on "dehn.mth.pdx.edu" and "wuarchive.wustl.edu"):

-r--r--r-- 1 ftp 39155 Apr 28 10:32 weyl.tar.Z -r--r--r-- 1 ftp 40641 Apr 28 10:32 weyl.zoo

It features the following improvements:

----------------------------------------------------------------------------- Dear GAP-Forum, there are some small changes and one bug fix in the 'weyl' package. (However, every program written before should be 'upward compatible'.) You can see the changes in the following examples: # there are now non-cristallograhic (finite) Coxeter groups: gap> CartanMat("H",3); [ [ 2, E(5)^2+E(5)^3, 0 ], [ E(5)^2+E(5)^3, 2, -1 ], [ 0, -1, 2 ] ] gap> CartanMat("H",4); [ [ 2, E(5)^2+E(5)^3, 0, 0 ], [ E(5)^2+E(5)^3, 2, -1, 0 ], [ 0, -1, 2, -1 ], [ 0, 0, -1, 2 ] ] gap> CartanMat("I2",5); [ [ 2, E(5)^2+E(5)^3 ], [ E(5)^2+E(5)^3, 2 ] ]

# there is now an 'operations' component in the Weyl group record so that

# certain generic functions for domains will work for Weyl groups as well:

gap> W:=Weyl(last); Weyl( [ [ 2, E(5)^2+E(5)^3 ], [ E(5)^2+E(5)^3, 2 ] ] )

gap> RecFields(W);

[ "isDomain", "isWeylGroup", "cartan", "dim", "degree", "N", "roots",

"matgens", "permgens", "parameter", "operations" ]

gap> Size(W); 10

Some other changes improve the algorithms for computing Kazhdan-Lusztig

polynomials and for calculations in Hecke algebras (which were rather

slow before). E.g., on our HP computer, the command

'LeftCells( Weyl ( CartanMat( "F", 4 ) ) );'

now takes roughly 5 hours cpu time.

There was a bug in the programs for calculating in Hecke algebras, namely

in the program which computed the inverse of a standard basis element.

These changes were motivated by reports from other users. I should be very

glad about any further such comments and suggestions for improvements.

Aachen, 28.4.93, Meinolf Geck

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