Characteristic-free representation theory of the general linear group II. Homological considerations
1988; Elsevier BV; Volume: 72; Issue: 2 Linguagem: Inglês
10.1016/0001-8708(88)90027-8
ISSN1090-2082
AutoresKaan Akın, David A. Buchsbaum,
Tópico(s)Advanced Combinatorial Mathematics
ResumoIn our first paper of this series Cl], we indicated how we were led to consider resolutions of Schur and Weyl modules of a particular form. In order to prove the existence of these resolutions, we were forced to enlarge the family of skew shapes to a class J containing new shapes whose corresponding Schur and Weyl modules had heretofore not been studied. With these shapes in hand, we proved in [ 1 ] the existence of some fundamental exact sequences and described how, from these exact sequences, we could use a mapping cone construction to build up the resolutions we were seeking. For this mapping cone construction, we needed maps, and to provide maps we needed projectivity of tensor products of divided powers. This led to the study of the Schur algebra and its decomposition into orthogonal idempotents. In Sections 1 and 2 we review the information about the Schur algebra that we need to carry out our program. Fortunately there is a very clear and detailed exposition of this subject in the notes of J. A. Green [S] from which we borrowed very heavily.’ In fact, the main function of the first two sections is to condense and translate into our notation and terminology the relevant sections of Green’s notes. In Sections 3 and 4 we define the family of shapes, J, that we will study,
Referência(s)