Representations of Schur algebra

Postgraduate Thesis uoadl:2916015 305 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2020-06-07
Year:
2020
Author:
Evangelou Charalampos
Supervisors info:
Μαλιάκας Μιχαήλ, Καθηγητής του Τμήματος Μαθηματικών, ΕΚΠΑ (επιβλέπων)
Κοντογεώργης Αριστείδης, Καθηγητής του Τμήματος Μαθηματικών, ΕΚΠΑ
Εμμανουήλ Ιωάννης, Καθηγητής του Τμήματος Μαθηματικών, ΕΚΠΑ
Original Title:
Αναπαραστάσεις της Schur άλγεβρας
Languages:
Greek
Translated title:
Representations of Schur algebra
Summary:
In order to further study general linear group over the field of complex numbers, Schur algebra representations were introduced. This work originates from Shur's PhD study in 1901.

In this thesis we mainly study the followings:

1) An extensive study of the category of polynomial modules, the category of Schur modules, along with their corresponding relation.

2) Classification of irreducible modules relative to the categories mentioned in 1) as well as a study of their characters with main result over the fields of zero charactiristic.

3) Study of the Carter-Lusztig modules along with their correspoding relation relative to the categories mentioned in 1). The latter study along with the Carter-Lusztig lemma will enable the proof of basis theorem, which is the main result of this study.

4) Study of the representations of symmetric group over fields of characteristic zero or prime number p > 0. Main result of this study is Clausen-James theorem which relates fields of characteristic p > 0.
Main subject category:
Science
Keywords:
Schur algebra, Contravariant Duality, Weights, Characters, irreducible ΚΓ-modules, Carter-Lusztig modules, Specht modules, Schur functor, irreducible KG(r)-modules.
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
24
Number of pages:
267
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