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On Commutation Classes of Reduced Words in Weyl Groups

✍ Scribed by Robert Bédard

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
483 KB
Volume
20
Category
Article
ISSN
0195-6698

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✦ Synopsis

This paper is concerned with commutation classes of reduced words in Weyl groups. It is divided in three sections. In the first, we give a recursive formula for the number of reduced words in a commutation class. In the second, we give a tableau-like description of all the reduced words adapted to a quiver in the case of simply laced root system. In the last, we consider the case of the longest element w 0 for the symmetric group S 5 and illustrate the fact that the set of commutation classes of reduced words of w 0 have nice symmetries and a topological structure.

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