Youngove tablice

diplomsko delo

Nina Jelen (Author), Dušan Pagon (Mentor)

Abstract

V diplomskem delu bom predstavila Youngove tablice, ki so v upodobitveni teoriji zelo uporaben objekt. Uporabljajo se tudi v kombinatoriki in algebrski teoriji. So zelo priročne za upodobitev simetričnih in splošnih linearnih grup in za preučevanje njihovih lastnosti. Veliko dejstev o upodobitvah lahko izpeljemo iz ustreznih diagramov, na primer določitev dimenzije upodobitve in omejitve upodobitve Sn na podgrupah. V obeh primerih se vidi, da veliko lastnosti upodobitve lahko razberemo že iz njene tablice. Predstavljeni so tudi poševno simetrični diagrami, ki jih dobimo z odstranjevanjem manjših Youngovih diagramov iz večjih in kako se konstruirajo nerazcepne upodobitve simetričnih grup nad poljubnim poljem. Na koncu so navedene tudi vse nerazcepne upodobitve simetrične grupe S3.

Keywords

matematika;Youngove tablice;diagrami;poševno simetrični diagrami;upodobitve;simetrične grupe;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Jelen]
UDC:	51(043.2)
COBISS:	17740040
Views:	1977
Downloads:	165
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	YOUNG TABLEAUX
Secondary abstract:	In my thesis I present the Young tableaux, which are in the representation theory a very useful subject. They are also used in combinatorics and algebraic theory. They are very convenient for the representation of symmetric and general linear groups and they have also been usable when studying their properties. Many facts about the representations can be derived from the corresponding diagrams, such as the determination of the dimension of the representation and restriction of Sn on subgroups. In both cases one can see that many properties of the representation can already be made out from its tableaux. I have also represented skew diagrams, which are obtained by removing smaller Young's diagrams from the larger ones and how to construct irreducible representations of symmetric groups over an arbitrary field. In the end I have quoted all irreducible representations of symmetric group S3.
Secondary keywords:	Young tableaux;Young diagrams;skew diagrams;representation theory of the symmetric group;irreducible representation.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 28 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18598