REPTHOX · Representation theory of Schur algebras
6РП — Действия „Мария Кюри“
- Период
- 2007-09-01 → 2009-08-31
- Финансиране от ЕС
- 152 809 €
- Участници
- 1
- Схема
- EIF
Линиите свързват координатора с партньорите.
Накратко на български
Алгебричните структури на симетриите се изследват чрез т.нар. алгебри на Шура, като например при трансформирането на двуизмерно пространство. Тези анализи помагат за по-доброто разбиране на общите линейни групи и техните свойства.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - REPTHOX (Representation Theory of Schur algebras)
This project studies algebraic structures arising from symmetries by their actions on spaces. One such algebraic structure of particular importance is the general linear group, the group of all invertible transformations of a space which fixes the origin. In this project, the representation theory of general linear group was studied. This is encoded in so-called Schur algebras. For the general linear group of a two-dimensional space, the participants have explicitly described all Schur algebras in a way that gives combinatorial access to the most important (namely projective) representations by exhibiting higher symmetries. They have furthermore, for general linear groups of a space of arbitrary dimension, given an algorithm for computing the objects of another important subclass of representations - the so-called standard filtered modules. Various other results investigating certain invariants of Schur algebras and related algebras add to the improved understanding of these fundamentally important groups.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
Two of the central problems in the representation theory of reductive algebraic groups are, firstly, to understand simple representations and their characters (in particular, to determine the so-called decomposition numbers), and, secondly, to determine ex tensions between simple representations, thus aiming to describe indecomposable ones.Schur algebras are a class of finite-dimensional algebras whose representation theory encapsulates the representation theory of (infinite) reductive algebraic groups. This project will focus on the ring theoretic structure and cohomological properties of Schur algebras and will cover both characteristic independent and characteristic dependent situations. This algebraic approach is different from the geometric approach, as taken in Kazhdan-Lusztig theory, where small characteristics are not covered.The proposed research will combine two main objectives.- The first objective will provide a practicable description of a certain triangulated subcategory of the derived category of hereditary which - applied to Schur algebras - will allow us to explicitly compute extensions between Weyl modules, thus gaining information about decomposition numbers.- The second objective will then focus on structural information on Schur algebras, namely Morita equivalences between sub-and factor algebras and in particular between blocks.The project will be carried out at the Mathematical Institute in Oxford under the supervision of Dr Erdmann and Dr Henke, who are both experienced researchers in the field.
Оригинален текст от CORDIS (на английски).
Участници
- THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD · OXFORDКоординаторОбединеното кралство
Връзки
Данни: CORDIS, © Европейски съюз