# Left cells in the affine Weyl group of type C~4

## Author

**Jian-yi Shi**

## Status

Research Report 97-21

Date: 12 July 1996, revised 2 May 1997

## Abstract

We find a representative set of left cells of the affine Weyl group Wa of type
C~4 as well as its left cell graphs by applying an algorithm. This algorithm
was designed in my previous paper [22]. It is reformulated and improved in
more efficient form here. These representatives of left cells are presented as
the vertices of so called essential graphs so that the generalized
T-invariants of left cells of Wa are actually described explicitly, the latter
almost characterize the left cells of Wa. Some comments and conjectures are
proposed on cells of affine Weyl groups, mostly for the case of type C~m, m>1.

## Key phrases

affine Weyl group. left cell. left cell graph. generalized T-invariants.

## AMS Subject Classification (1991)

Primary: 20H55

Secondary: 20H15

## Content

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