Уваров Ф.В. - Группы и Алгебры Ли - 10. Representation theory of sl(2)

00:00:15 Reminder of the previous lectures 00:00:44 Introduction of representation theory 00:13:40 Proposition: Lie is bijective if G is connected 00:14:28 Proof of the proposition 00:30:55 Definition 1: subrepresentation of (r,V)) 00:32:37 Definition 2: irreducible subrepresentation 00:34:01 Definition 3: completely reducible subrepresentation 00:36:40 Plan of representation theory part of lectures 00:37:01 Repeat all the definitions for algebras 00:42:25 Schur’s lemma 00:44:26 Proof of the Schur’s lemma 00:51:26 Representation of sl(2,C) 00:53:20 Proposition 2: about finite-dim irreducible representation of sl(2,C) 00:55:05 Proof the the proposition 2 01:12:24 Definition 4: weight vector 01:14:08 Definition 5: singular vector 01:14:35 Proposition 3: singular vector of weight 01:18:14 Proof of the proposition 3 01:25:03 Definition 6: highest weight vector 01:26:08 Uniqueness of the highest weight vector 01:30:10 Proposition 4: the map is bijective Ссылка на плейлист: #мгу #мехмат #уваров #группыли #алгебрыли