Name | Prof. em. Dr. Giovanni Felder |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG G 46 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 34 09 |

giovanni.felder@math.ethz.ch | |

URL | http://www.math.ethz.ch/~felder |

Department | Mathematics |

Relationship | Professor emeritus |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3160-68L | Representation Theory: Groups, Algebras and Quivers Number of participants limited to 14. | 4 credits | 2S | G. Felder, further speakers | |

Abstract | Representation theory of groups, algebras, quivers, based on examples and solving problems. | ||||

Objective | The students will learn basic notions and techniques of representation theory and to apply these techniques in concrete situations and examples. | ||||

Content | Introduction to representation theory with many examples. Lie algebras and universal enveloping algebra. Schur lemma, representations of a matrix algebra. Jordan-Holder theorem, extensions. Category O for sl(2). Representations of finite groups. Burnside theorem, Frobenius reciprocity. Representations of symmetric groups. Representations of GL_2(F_q). Quivers. McKay correspondence. | ||||

Literature | The main reference is: [E] P.Etingof, O. Goldberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina, Introduction to representation theory, with historical interludes by S. Gerovitch, AMS 2010. Much of the material (but not the historical interludes) can be found at http://math.mit.edu/~etingof/replect.pdf Additional literature that might be helpful: [F] W.Fulton, Representation theory, A first course. [L] S. Lang, Algebra. [S] J-P. Serre, Lie Algebras and Lie Groups [BGP] I N Bernstein, I M Gel'fand and V A Ponomarev "COXETER FUNCTORS AND GABRIEL'S THEOREM" Russ. Math. Surv. 28 [D] Igor Dolgachev McKay's correspondence for cocompact discrete subgroups of SU(1,1) available at http://arxiv.org/pdf/0710.2253 | ||||

Prerequisites / Notice | Linear algebra and basic notions of algebra. Please refresh (or learn) basic notions of multilinear algebra to be able to solve the first problems on tensor products of vector spaces in [E]. Each participant gives a presentation and is assigned a set of exercises, whose solution is published on the wiki of the seminar. | ||||

401-5330-00L | Talks in Mathematical Physics | 0 credits | 1K | A. Cattaneo, G. Felder, M. Gaberdiel, G. M. Graf, T. H. Willwacher, University lecturers | |

Abstract | Research colloquium | ||||

Objective |