Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.290191
Title: Some subalgebras of the Schur algebra
Author: Santana, Ana Paula Jacinto
ISNI:       0000 0001 3551 7358
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1990
Availability of Full Text:
Access from EThOS:
Access from Institution:
Abstract:
In this thesis we study some subalgebras of the Schur algebra for the general linear group GLn(k) particularly the Schur algebra S(B+) for the Borel subgroup B+ of GLn(k). In many ways it is easier to work in S(B+) than in the more complicated algebra S(GLn(k). Using the properties of S(B+) we give a new treatment of the Weyl modules for GLn(k). We then construct 2-step minimal projective resolutions of the irreducible S(B+)-modules and from these we obtain very easily 2-step projective resolutions of the Weyl modules for GLn(k). We study the Cartan invariants of S(B+) and show that under certain conditions they satisfy an interesting identity. For particular cases of the field k and of the integer n we prove several results on minimal projective resolutions of the irreducible S(B+)-modules. The methods we use are combinatorial and do not involve algebraic group theory.
Supervisor: Not available Sponsor: Fundação Calouste Gulbenkian
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.290191  DOI: Not available
Keywords: QA Mathematics
Share: