Santana, Ana Paula Jacinto (1990) Some subalgebras of the Schur algebra. PhD thesis, University of Warwick.

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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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Algebra, Representations of groups, Combinatorial analysis
Official Date:	May 1990
Dates:	Date Event May 1990 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Green, J. A. (James Alexander)
Sponsors:	Fundação Calouste Gulbenkian
Format of File:	pdf
Extent:	[159] leaves : illustrations
Language:	eng

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