The Library
Classes of maximal-length reduced words in Coxeter groups
Tools
Tools
Tools
Scott, Anthony (1996) Classes of maximal-length reduced words in Coxeter groups. PhD thesis, University of Warwick.
|
PDF
WRAP_THESIS_Scott_1996.pdf - Submitted Version - Requires a PDF viewer. Download (55Mb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b1402578~S1
Abstract
This thesis is concerned with the graph R of all reduced words for the longest element in the Coxeter groups of classical type, the edges representing braid relations.
In chapter 2 we consider the equivalence relation on the vertices of R generated by commuting adjacent letters if the corresponding simple reflections commute. An inductive way of describing all of the resulting commutation classes is described.
A characterisation of the quiver-compatible commutation classes, couched in terms of letter-multiplicities, is presented in chapter 3.
Chapter 4 introduces for each positive root ß an equivalence relation on R whose equivalence dasses are connected subgraphs called ß-components. It is shown that the ß-components are in bijective correspondence with the root vectors for ß (following Bedard) when ß is the highest root ∝0; in general there are more ß-components.
It happens that the natural quotient graph of ß-components is determined up to isomorphism by the length of ß; we choose to focus on the ∝0-components.
In chapter 5 we show that each ∝0-component in type A1, contains a unique quiver-compatible commutation class.
In chapter 6 we count the ∝0-components in type B1, by exhibiting explicit representatives which have a natural interpretation as partial quivers.
The edges of the graphs of ∝0-components in types A1, and B1, are determined by interpreting maximal chains in certain posets as elements of the Coxeter group of type A1-2 or B1-2, respectively.
Chapter 7 establishes an isomorphism between the graphs of ß-components in types B1 and D1 whenever ß is long.
| Item Type: | Thesis or Dissertation (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Coxeter groups | ||||
| Official Date: | August 1996 | ||||
| Dates: |
|
||||
| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Carter, Roger W. (Roger William) | ||||
| Sponsors: | Engineering and Physical Sciences Research Council | ||||
| Extent: | 105 leaves | ||||
| Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
