MAT 543 — Fall 2025 Problem Sets MAT 543 — Fall 2025 Schedule

MAT 543 Course Webpage
Representation Theory
M W 2 PM — 3:20 PM, Math Tower 4—130

Fall 2025
  • Problem sets
  • Syllabus
  • Course Announcements
  • Course Description
  • Prerequisites
  • Text
  • Lectures
  • Office Hours
  • Grading System
  • Disability Support Services
  • Academic Integrity
  • Critical Incident Management

    • Course Announcements Announcements about the course will be posted here. Please check the site regularly for announcements (which will also be given in lecture).

    Course Description An introduction to representation theory, with a focus on explicit examples. Representations of finite groups (in characteristic zero), especially symmetric and alternating groups. Representation theory of compact Lie groups and semisimple Lie algebras (which may also be covered in MAT 552). Representations of classical groups, esp. GL(n) and orthogonal groups. Schur-Weil duality for representations of S_n and GL(n), Young diagrams. Other possible topics include spin representations and Clifford algebras, representations of exceptional groups, applications to physics (e.g. hydrogen atom, spin, quarks), or an introduction to invariant theory.

    Prerequisites MAT 535, or permission of instructor. Familiarity with material covered by MAT 552 would be helpful, but is not required.

    Text Although it is not listed as a required textbook, this semester the course will closely follow the textbook by Fulton and Harris.

    Lectures The instructor for this course is Jason Starr. All instruction will occur in lectures. A tentative schedule will be posted in the schedule.

    Lecture is held Mondays and Wednesdays, 2 PM — 3:20 PM in Math Tower 4—130.

    Office Hours Here is a link to the current office hours.

    Grading System As will be discussed at the first class meeting, grading will be based on class participation and problem sets.

    Required Syllabi Statements
    The University Senate Undergraduate and Graduate Councils have authorized that the following required statements appear in all teaching syllabi (graduate and undergraduate courses) on the Stony Brook Campus.

    Student Accessibility Support Center (SASC) statement

    If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748 or at sasc@Stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Student Accessibility Support Center Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and SASC. For procedures and information go to the following website: Evacuation guide for people with physical disablilities

    Academic Integrity

    Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at Academic Judiciary

    Critical Incident Management

    Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.

    Back to my home page.

    Jason Starr
    4-108 Math Tower
    Department of Mathematics
    Stony Brook University
    Stony Brook, NY 11794-3651
    Phone: 631-632-8270
    Fax: 631-632-7631
    Jason Starr