2018 Advanced topics in Geometry H

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Honda Nobuhiro 
Course component(s)
Lecture     
Day/Period(Room No.)
Fri5-6(H103)  
Group
-
Course number
MTH.B504
Credits
1
Academic year
2018
Offered quarter
4Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
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Course description and aims

We explain basic materials in representation theory on compact Lie groups. This course is a continuation of MTH.B503.

Student learning outcomes

Understand basics on Lie groups and Lie algebras with various examples

Keywords

adjoint representation, invariant measure, Schur's lemma, characters, Schur orthogonality relations

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

standard lecture course

Course schedule/Required learning

  Course schedule Required learning
Class 1 adjoint representation, invariant measure Details will be provided during each class session
Class 2 Schur's lemma
Class 3 representation theory of SU(2)
Class 4 characters, Schur's orthogonality relation
Class 5 fundamental properties of characters
Class 6 representation theory of SU(2) and su(2)
Class 7 representation theory of SU(2) and su(2) (continued)
Class 8 product representation, representation of SO(4)

Textbook(s)

none

Reference books, course materials, etc.

Warner, "Foundation of differential manifolds and Lie groups" GTM 94, Chapter 3

Assessment criteria and methods

homework

Related courses

  • MTH.B503 : Advanced topics in Geometry G

Prerequisites (i.e., required knowledge, skills, courses, etc.)

none

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