Homogeneous Projective Varieties of Rank 2 Groups

Homogeneous Projective Varieties of Rank 2 Groups

Show other versions (2)

Root systems are a fundamental concept in the theory of Lie algebra. In this thesis, we will use two different kind of graphs to represent the group generated by reflections acting on the elements of the root system. The root systems we are interested in are those of type A2, B2 and G2. After drawin...

Full description

Bibliographic Details
Main Author: Leclerc, Marc-Antoine
Language:en
Published: 2012
Subjects:
Lie Algebra
Root System
Weyl Group
Pieri Graph
Algebraic Group
Representation Theory
Chow Group
Online Access:http://hdl.handle.net/10393/23558
id ndltd-LACETR-oai-collectionscanada.gc.ca-OOU.#10393-23558
record_format oai_dc
spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OOU.#10393-235582014-06-12T03:51:06ZHomogeneous Projective Varieties of Rank 2 GroupsLeclerc, Marc-AntoineLie AlgebraRoot SystemWeyl GroupPieri GraphAlgebraic GroupRepresentation TheoryChow GroupRoot systems are a fundamental concept in the theory of Lie algebra. In this thesis, we will use two different kind of graphs to represent the group generated by reflections acting on the elements of the root system. The root systems we are interested in are those of type A2, B2 and G2. After drawing the graphs, we will study the algebraic groups corresponding to those root systems. We will use three different techniques to give a geometric description of the homogeneous spaces G/P where G is the algebraic group corresponding to the root system and P is one of its parabolic subgroup. Finally, we will make a link between the graphs and the multiplication of basis elements in the Chow group CH(G/P).2012-11-29T18:01:17Z2012-11-29T18:01:17Z20122012-11-29Thèse / Thesishttp://hdl.handle.net/10393/23558en
collection NDLTD
language en
sources NDLTD
topic Lie Algebra
Root System
Weyl Group
Pieri Graph
Algebraic Group
Representation Theory
Chow Group
spellingShingle Lie Algebra
Root System
Weyl Group
Pieri Graph
Algebraic Group
Representation Theory
Chow Group
Leclerc, Marc-Antoine
Homogeneous Projective Varieties of Rank 2 Groups
description Root systems are a fundamental concept in the theory of Lie algebra. In this thesis, we will use two different kind of graphs to represent the group generated by reflections acting on the elements of the root system. The root systems we are interested in are those of type A2, B2 and G2. After drawing the graphs, we will study the algebraic groups corresponding to those root systems. We will use three different techniques to give a geometric description of the homogeneous spaces G/P where G is the algebraic group corresponding to the root system and P is one of its parabolic subgroup. Finally, we will make a link between the graphs and the multiplication of basis elements in the Chow group CH(G/P).
author Leclerc, Marc-Antoine
author_facet Leclerc, Marc-Antoine
author_sort Leclerc, Marc-Antoine
title Homogeneous Projective Varieties of Rank 2 Groups
title_short Homogeneous Projective Varieties of Rank 2 Groups
title_full Homogeneous Projective Varieties of Rank 2 Groups
title_fullStr Homogeneous Projective Varieties of Rank 2 Groups
title_full_unstemmed Homogeneous Projective Varieties of Rank 2 Groups
title_sort homogeneous projective varieties of rank 2 groups
publishDate 2012
url http://hdl.handle.net/10393/23558
work_keys_str_mv AT leclercmarcantoine homogeneousprojectivevarietiesofrank2groups
_version_ 1716668932959502336

Similar Items