Special Mathematics Lecture

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 237 in Sci. Bldg. A

Groups and their representations (Spring 2018)

Registration code : 0053621
Schedule : Wednesday (18:30 - 20.00) in room 207 of the Science Building A
Registration: See page 15 of this document

• Syllabus : the pdf file

• Class dates :
  April 11, 18, 25
  May 2, 9, 16, 23, 30
  June 6, 13, 20, 27
  July 4, 11, 18
  

• Program and notes taken by L. Zhang :
  1) Groups Summary on matrices, lect. 1, lect. 2, lect. 3
  2) Linear representations Summary on Hilbert spaces, lect. 3.5, lect. 4, lect. 5, lect. 6, lect. 7, lect. 8
  3) Lie groups lect. 8.5, lect. 9, lect. 10
  4) Semisimple theory lect. 11, lect. 12, lect. 13, lect. 14, lect. 15

• The cumulative notes taken by L. Zhang, with table of content : Groups and their representations

• At the end of the last lecture :
  

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Hideki Inoue

• Works submitted by the students :
  About normal subgroups and quotient groups, by Naohiro Tsuzu
  About subgroups, cosets, and homomorphims, by Keito Masuda
  Many proofs related to the 1st lecture, by Liyang Zhang
  On inner and outer semi-direct product, by Song Ha Nguyen and Dang Cong Bui
  On Aut(G), by Takuya Ishibashi
  About normal subgroups and homomorphisms, by Chang Sun
  On tensor product of Hilbert spaces, by Naohiro Tsuzu
  Transformation groups and finite subgroups of O(2) , by Liyang Zhang
  On nilpotent and solvable Lie algebras, by Takuya Ishibashi
  On generalized eigenvectors, by Shihab Fadda
  On su(n) and the Killing form, by Son Nguyen, Cong Bui, Song Ha
  About the complexification of a Lie algebra, by Sparsh Mishra
  On the Killing form, by Zhang Nuozhou
  On the Poincare group, by Adrien Levacic
  Universal enveloping algebras and Casimir operators, by Yoshihiko Terasawa
  On root system, by Cong Bui, Song Ha
  

• References : (electronic version available upon request)
  Lecture notes: Theorie des groupes pour la physique, written by W. Amrein. Excellent, but in French
  Book: Group theory in physics, an introduction, written by J.F. Cornwell. Looks appropriate. Based on previous volumes I and II
  Book: Functional analysis I, written M. Reed and B. Simon. A classical book of functional analysis
  Book: A course in the theory of groups, written by D.J. Robinson. More complicated and more complete, notations not so friendly
  Book: Representations of finite and compact groups, written by B. Simon. Excellent, but little bit advanced
  Book: Group theory and physics, written by S. Sternberg. Looks quite accessible
  Book: Lie groups, Lie algebras, and representations: an elementary introduction, written by B. Hall. Almost everything on linear Lie groups and algebras, quite accessible
  Book: Lie algebras in particle physics, from isospin to unified theories, written by H. Georgi. Written for physicists, but provides a good introduction with many heuristic explanations
  Lectures notes: Group theory (for physicists), written by C. Ludeling. Covers the main topics
  Lecture Notes: Group Theory Summary, written by M. Schaller. Very brief text
  Lecture notes: Group theory and its applications in physics, written by B. Gutkin. Much more physically oriented
  Lecture notes: Symmetries and groups, written by H. Osborn. More advanced, with material on gauge groups and gauge theories
  Lecture notes: Invariances in Physics and Group Theory, written by J.-B. Zuber. More advanced, with material on gauge theories