 
Course Information

Course Number:	Math 689
Course Title: Representation Theory of Lie groups and algebras	
Section:	
Time: MWF 10-11 (tent)	
Location: Blocker TBA	
Credit Hours:	

Instructor Details

Instructor:	Joseph M. Landsberg
Office:Blocker 601H	
Phone:	
E-Mail:jml@math.tamu.edu	
Office Hours: Tues. 10-11am, Thurs 2-3pm	

Course Description

This will be an introduction to the representation theory of Lie groups and
algebras, with an emphasis on geometric aspects.

Course Prerequisites

None for graduate students. Undergraduates wishing
to enroll need permission of the instructor.

Special Course Designation

None

Course Learning Outcomes

Students will be able to exploit symmetry in their research.

Textbook and/or Resource Materials

Required:

W. Fulton and J. Harris, "Representation Theory: a first course"
Springer-Verlag GTM 129

J. Humphreys, "Introduction to Lie Algebras and Representation Theory"
Springer-Verlag GTM 9

Grading Policy

Grades will be exclusively determined by homework and presentation of homework
in class. Each week there will be 3 mandatory homework problems to prepare
and numerous supplemental problems. Students will sign up to present problems
in class. Grade is 50% on written homework, 50% on presentation

Graded Class Participation – participation grade is 1/2 volunteering to present, 1/2 quality of presentation

Graded Attendance – N/A

Grades for Stacked Course – N/A

Grading Policy Changes – N/A
Late Work Policy

Late homework will not be accepted.
 Work submitted by a student as makeup work for an excused absence is not considered late work and is exempted from the late work policy. (See Student Rule 7.)

Course Schedule

Week 1: Introduction to Lie groups and algebras: definitions, examples
Week 2: Basic properties of Lie algebras:  semi-simple
and nilpotent Lie algebras, Lie's theorem, Engle's theorem.
Week 3: Representations of sl_2C and sl_3C
Week 4: Roots and weights
Week 5: Representations of sl_nC
Week 6: Representations of  orthogonal Lie algebras
Week 7: Representations of  symplectic Lie algebras
Weeks 8-9: Classification of complex simple Lie algebras
Week 10: Real Lie groups and algebras
Week 11: Universal enveloping algebra and the PBW theorem
Week 12: Theorem of the highest weight
Week 13: Harish-Chandra Theorem
Week 14: Weyl character formula and consequences
Week 15: Advanced topics

 

Optional Course Information Items

There will be a supplementary working seminar that will cover additional topics.



Technology Support – Provide appropriate technical support information to inform students who to contact if they encounter technical difficulties (e.g., direct technical questions to the course teaching assistant; contact the vendor; etc.). Technical support information should include information such as who to contact, how to contact that resource, hours of availability, etc. 

Learning Resources – Provide information regarding available learning resources such as supplemental instruction or tutoring when appropriate (e.g., information about the University Writing Center for a W/C designated course or related LinkedIn Learning modules appropriate for the course topic). The Study Hub website lists many on-campus learning resources to support students in achieving academic excellence.

University Policies

This section outlines the university level policies that must be included in each course syllabus. The TAMU Faculty Senate established the wording of these policies. 

NOTE: Faculty members should not change the written statements. A faculty member may add separate paragraphs if additional information is needed. 

Attendance Policy

The university views class attendance and participation as an individual student responsibility. Students are expected to attend class and to complete all assignments. 

Please refer to Student Rule 7 in its entirety for information about excused absences, including definitions, and related documentation and timelines.

Makeup Work Policy

Students will be excused from attending class on the day of a graded activity or when attendance contributes to a student’s grade, for the reasons stated in Student Rule 7, or other reason deemed appropriate by the instructor. 

Please refer to Student Rule 7 in its entirety for information about makeup work, including definitions, and related documentation and timelines.

Absences related to Title IX of the Education Amendments of 1972 may necessitate a period of more than 30 days for make-up work, and the timeframe for make-up work should be agreed upon by the student and instructor” (Student Rule 7, Section 7.4.1).

“The instructor is under no obligation to provide an opportunity for the student to make up work missed because of an unexcused absence” (Student Rule 7, Section 7.4.2).

Students who request an excused absence are expected to uphold the Aggie Honor Code and Student Conduct Code. (See Student Rule 24.)

Academic Integrity Statement and Policy

“An Aggie does not lie, cheat or steal, or tolerate those who do.”

“Texas A&M University students are responsible for authenticating all work submitted to an instructor. If asked, students must be able to produce proof that the item submitted is indeed the work of that student. Students must keep appropriate records at all times. The inability to authenticate one’s work, should the instructor request it, may be sufficient grounds to initiate an academic misconduct case” (Section 20.1.2.3, Student Rule 20).

You can learn more about the Aggie Honor System Office Rules and Procedures, academic integrity, and your rights and responsibilities at aggiehonor.tamu.edu.

NOTE: Faculty associated with the main campus in College Station should use this Academic Integrity Statement and Policy. Faculty not on the main campus should use the appropriate language and location at their site.

Americans with Disabilities Act (ADA) Policy

Texas A&M University is committed to providing equitable access to learning opportunities for all students. If you experience barriers to your education due to a disability or think you may have a disability, please contact Disability Resources in the Student Services Building or at (979) 845-1637 or visit disability.tamu.edu. Disabilities may include, but are not limited to attentional, learning, mental health, sensory, physical, or chronic health conditions. All students are encouraged to discuss their disability related needs with Disability Resources and their instructors as soon as possible.

NOTE: Faculty associated with the main campus in College Station should use this Americans with Disabilities Act Policy statement. Faculty not on the main campus should use the appropriate language and location at their site.

Title IX and Statement on Limits to Confidentiality

Texas A&M University is committed to fostering a learning environment that is safe and productive for all. University policies and federal and state laws prohibit gender-based discrimination and sexual harassment, including sexual assault, sexual exploitation, domestic violence, dating violence, and stalking.

With the exception of some medical and mental health providers, all university employees (including full and part-time faculty, staff, paid graduate assistants, student workers, etc.) are Mandatory Reporters and must report to the Title IX Office if the employee experiences, observes, or becomes aware of an incident that meets the following conditions (see University Rule 08.01.01.M1):

The incident is reasonably believed to be discrimination or harassment. 
The incident is alleged to have been committed by or against a person who, at the time of the incident, was (1) a student enrolled at the University or (2) an employee of the University. 

Mandatory Reporters must file a report regardless of how the information comes to their attention – including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Although Mandatory Reporters must file a report, in most instances, a person who is subjected to the alleged conduct will be able to control how the report is handled, including whether or not to pursue a formal investigation. The University’s goal is to make sure you are aware of the range of options available to you and to ensure access to the resources you need.

Students wishing to discuss concerns in a confidential setting are encouraged to make an appointment with Counseling and Psychological Services (CAPS). 

Students can learn more about filing a report, accessing supportive resources, and navigating the Title IX investigation and resolution process on the University’s Title IX webpage.

NOTE: Faculty associated with the main campus in College Station should use this Title IX and Statement on Limits of Liability. Faculty not on the main campus should use the appropriate language and location at their site.

Statement on Mental Health and Wellness

Texas A&M University recognizes that mental health and wellness are critical factors that influence a student’s academic success and overall wellbeing. Students are encouraged to engage in healthy self-care by utilizing the resources and services available from Counseling & Psychological Services (CAPS). Students who need someone to talk to can call the TAMU Helpline (979-845-2700) from 4:00 p.m. to 8:00 a.m. weekdays and 24 hours on weekends. 24-hour emergency help is also available through the National Suicide Prevention Hotline (800-273-8255) or at suicidepreventionlifeline.org. 

College and Department Policies

College and departmental units may establish their own policies and minimum syllabus requirements. As long as these policies and requirements do not contradict the university level requirements, colleges and departments can add them in this section.