CANONICAL LEFT CELLS AND THE SHORTEST LENGTH ELEMENTS IN THE DOUBLE COSETS OF WEYL GROUPS

- Journal title : Honam Mathematical Journal
- Volume 33, Issue 1, 2011, pp.19-25
- Publisher : The Honam Mathematical Society
- DOI : 10.5831/HMJ.2011.33.1.019

Title & Authors

CANONICAL LEFT CELLS AND THE SHORTEST LENGTH ELEMENTS IN THE DOUBLE COSETS OF WEYL GROUPS

Kwon, Nam-Hee;

Kwon, Nam-Hee;

Abstract

Let G be the general linear group GL(n,), the Weyl group of G and W the extended a neWeyl group of G. Then it is well-known that W is a union of the double cosets as x moves over the set of dominant weights of W. It is also known that each double coset contains a unique element of the shortest length. These shortest length elements belong to what are called the canonical left cells. However, it is still an open problem to find the canonical left cell containing a given . One of the mai purposes of this paper is to introduce a new approach to attack this question. In particular, we will present a conjecture which explicitly describes the canonical left cells containing an element . We will show that our conjecture is true for some specific types of .

Keywords

Weyl group;two-sided cell;canonical left cell;

Language

English

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