Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Στεργιοπούλου Δήμητρα-Διονυσία
Supervisors info:
Μιχάλης Μαλιάκας Καθηγητής
Original Title:
Προβολικές επιλύσεις των αναπαραστάσεων της GL_n
Translated title:
Projective resolutions of representations of GL_n
Summary:
We consider polynomial representations of GL_n over a fild K and intoduce the
corresponding Schur algebra, wich is of finite dimension. We use the fact that
the category of homogeneous polynomial representations of GL_n of degree r is
equivalent to the category of S(n,r)-modules, where S(n,r) is the corresponding
Schur algebra of degree r. The main problem is the value of the global
homological dimension of S(n,r). Firstly we calculate a suitable upper bound
and then we find a S(n,r)-module whose projective dimension equals to this
upper bound.
Keywords:
Polynomial representations, Schur algebra, Projective resolutions, Global dimension, GL_n
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