The Library
Integral forms for Weyl modules of GL(2,Q)
Tools
Stevens, Perdita (1992) Integral forms for Weyl modules of GL(2,Q). PhD thesis, University of Warwick.

PDF
WRAP_Theses_Stevens_1992.pdf  Submitted Version  Requires a PDF viewer. Download (2871Kb)  Preview 
Official URL: http://webcat.warwick.ac.uk/record=b3252359~S15
Abstract
In this thesis we determine the integral forms in Weyl modules for GL(2,Q). We work with the Schur algebra exclusively; we do not use the Lie algebra of GL(2,Q).
In Chapter 1 we give the necessary background. We begin to simplify the problem, using the known reduction of it to the problem of finding those integral forms which lie between certain limits Y and V. Together with localisation at each prime p, this enables us to restrict our attention to the structure of X/Vp. We show that we can deduce the integral structure of any Weyl module from that of Weyl modules with highest weight (r, 0) for an integer r. We describe a duality which arises on X/Vp. In Chapter 2 we prove a rather surprising numbertheoretic result which allows us to simplify the problem further. In Chapter 3 we arrive at a very simple characterisation of the integral forms, namely that they can be represented as those integer labellings of a particular graph, the scoreable set lattice, which satisfy a certain criterion. We exploit this to prove various general results about the structure of X/Vp. We show how it is possible, using our methods, to describe the structure of X/Vp in arbitrarily complicated cases in terms of simpler structures. In Chapter 4, we discuss the relevance of our work to the theory of modular Weyl modules, and we explain how our work relates to that of others.
Item Type:  Thesis (PhD)  

Subjects:  Q Science > QA Mathematics  
Library of Congress Subject Headings (LCSH):  Representations of algebras, Representations of groups, Schur functions, Weyl groups, Modules (Algebra)  
Official Date:  June 1992  
Dates: 


Institution:  University of Warwick  
Theses Department:  Mathematics Institute  
Thesis Type:  PhD  
Publication Status:  Unpublished  
Supervisor(s)/Advisor:  Green, J. A. (James Alexander)  
Sponsors:  Science and Engineering Research Council (Great Britain)  
Format of File:  
Extent:  iv, 120 leaves : illustrations  
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