Giovanni Felder: Katalogdaten im Herbstsemester 2018

Auszeichnung: Die Goldene Eule
NameHerr Prof. em. Dr. Giovanni Felder
LehrgebietMathematik
Adresse
Professur für Mathematik
ETH Zürich, HG G 46
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 34 09
E-Mailgiovanni.felder@math.ethz.ch
URLhttp://www.math.ethz.ch/~felder
DepartementMathematik
BeziehungProfessor emeritus

NummerTitelECTSUmfangDozierende
401-3160-68LRepresentation Theory: Groups, Algebras and Quivers Belegung eingeschränkt - Details anzeigen
Number of participants limited to 14.
4 KP2SG. Felder, weitere Referent/innen
KurzbeschreibungRepresentation theory of groups, algebras, quivers, based on examples and solving problems.
LernzielThe students will learn basic notions and techniques of representation theory and to apply these techniques in concrete situations and examples.
InhaltIntroduction 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.
LiteraturThe 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
Voraussetzungen / BesonderesLinear 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.
401-5330-00LTalks in Mathematical Physics Information 0 KP1KA. Cattaneo, G. Felder, M. Gaberdiel, G. M. Graf, T. H. Willwacher, Uni-Dozierende
KurzbeschreibungResearch colloquium
Lernziel