Department of Mathematics
MA 792J-002 – Representations of infinite-dimensional Lie
algebras
Spring 2009, MWF 2:30-3:20 pm, HA
272
Instructor: Dr. Bojko
Bakalov, office HA 138, phone 513-7442, email
bojko_bakalov at ncsu dot
edu
Office Hours: MF 1:30-2:25, W 3:20-4:00 or by appointment, in HA 138.
Prerequisite: Lie algebras (MA 720).
Course Description: This course is a follow-up
to MA
720 and is complementary to MA 725. Infinite-dimensional Lie algebras have connections and
applications to diverse areas of mathematics and physics such as:
combinatorics, group theory, number theory, soliton equations, quantum field
theory, and string theory. The Lie algebras we will discuss include the
Heisenberg, affine Kac-Moody and Virasoro algebras, as well as the Lie algebra
of infinite matrices. We will investigate their representations and characters,
and point out connections to combinatorial identities and modular functions.
Text: Bombay Lectures on Highest
Weight Representations of Infinite Dimensional Lie Algebras, by V.G. Kac
and A.K. Raina, World Scientific, 1987, ISBN-13: 978-9971503963
Web Resources: WolfWare
(Grade Book and Feedback), calendars and exam
schedules, math
courses, history of
mathematics.
Syllabus can be found here, and a tentative plan of the lectures here.
Homework will
be assigned regularly and will be collected every Friday at 2:30 pm.
Collaboration on the homework is allowed but everyone should write their own
solutions. Selected problems will be discussed in class.
Presentation: At the end of the course every student will have
to give a presentation on a topic related to but not covered in the lectures.
The topics will be chosen about a month in advance with the help of the
instructor. Here is a list of suggested topics.
Grade will be based on the homework (50%), presentation
(40%), and attendance and class participation (10%).
Attendance: Students are expected to arrive on time, to
contribute to group work and class discussions, and to stay until the class
ends. Attendance at all meetings of the class is expected and will be recorded.
Occasional absences will be approved if they meet University
policies.
Adverse Weather: Announcements regarding scheduled delays or the
closing of the University due to adverse weather conditions will be broadcast
on local radio and television stations and posted on the University homepage.
Cell Phones: Pagers, cellular phones and other types of
telecommunication equipment are prohibited from use during class. Make sure
that any pagers, phones or other equipment are turned off during the class
period. If you have a special need to have your pager or phone on during class,
please let me know.
Academic Integrity
Statement: Students are required
to follow the NCSU
policy. “Academic dishonesty is the giving, taking, or presenting
of information or material by a student that unethically or fraudulently aids
oneself or another on any work which is to be considered in the determination
of a grade or the completion of academic requirements or the enhancement of
that student's record or academic career.’’ (NCSU Code of Student Conduct).
The Student Affairs website
has more information.
Students with
Disabilities: Reasonable
accommodations will be made for students with verifiable disabilities. In order
to take advantage of available accommodations, students must register with Disabilities
Services for Students. Click here
for more information on the NCSU policy on working with students with
disabilities.
Class Evaluations: Online class evaluations will be available for
students to complete during the last two weeks of class. Students will receive an email message
directing them to a website where they can login using their Unity ID and
complete evaluations. All evaluations are
confidential; instructors will never know how any one student responded to any
question, and students will never know the ratings for any particular
instructors.