20.500.12556/DKUM-13969 YOUNGOVE TABLICE YOUNG TABLEAUX V diplomski nalogi bom predstavila Youngove tablice, ki so v upodobitveni teoriji zelo uporaben objekt. Uporabljajo pa se tudi v kombinatoriki in algebrski teoriji. So zelo priročne za upodobitev simetričnih in splošnih linearnih grup ter 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. 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. Youngove tablice Youngovi diagrami poševno simetrični diagrami upodobitve simetričnih grup nerazcepne upodobitve. Young tableaux Young diagrams skew diagrams representation theory of the symmetric group irreducible representation. true true false [N. Jelen] Slovenski jezik Angleški jezik Diplomsko delo 2010-05-14 12:57:57 2010-07-08 16:40:27 2022-04-12 11:38:00 2023-12-17 03:08:38 2010 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 17740040 URN:SI:UM:DK:UPCHZLIR UNI_Jelen_Nina_2010.pdf UNI_Jelen_Nina_2010.pdf 1 CA12A268B4B489929ECF689B53DD2AD4 934edecb8ea8ce90c51010e016d94ca18904507e84e1a0997648ba044e3523dd 09ece7cc-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/f574ff16-4230-4899-bfbd-8805e1937c3b https://dk.um.si/Dokument.php?lang=slv&id=14549 Fakulteta za naravoslovje in matematiko 0 0 0