Here is some basic information about this web page. (This web page is under construction - last update: November 13, 2009.)
I created this web page in the August of 2009 for a fall seminar/course at Iowa State University. You can look at the seminar announcement: Announcement. This seminar should be of interest to students and researchers in mathematics, physics and chemistry. Students can get credit for this seminar/course.
This seminar/course will meet at the following times and places starting Tuesday, September 1: Tuesdays, 10:00-10:50 in Carver 204; Thursdays, 10:00-10:50 in Carver 204 and 1:10-2:00 in Carver 190.
We shall study matrix groups. In particular, we shall mainly discuss the following book: B. Hall, "Lie Groups, Lie Algebras, and Representations - An Elementary Introduction", Springer, 2003.
Here is a list of the seminar talks.Nov. 19: Ken Driessel, "An Application of the Representations of SU(3) in Quantum Mechanics".
We discuss the use of representations in physics. In particular, we discuss the eight-fold way in quantum mechanics. Here are some references: Sternberg, S., 'Group theory and physics', Cambridge Univ. Press, 1994; Feynman, R., 'Lectures on Physics, Volume III, Quantum Mechanics', Addison-Wesley, 1965; Sattinger, D.H. and Weaver, O.L., 'Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics', Springer, 1986.
Nov. 17: Ken Driessel, "Representations of the Special Unitary Group SU(3)".
Abstract: We continue to discuss representations of SU(3). In particular, we continue discussing Chapter 5 in Hall's book.
Nov. 12: Ken Driessel, "Representations of SU(3)".
Abstract: We start discussing the fifth chapter in Hall's book.
Nov. 10: Ken Driessel, "Representations of Special Unitary Group SU(2)".
Abstract: We finally begin discussing the representations of the special unitary groups SU(2) and SU(3). Last week we did not get to this topic. We tied up some loose ends instead. In particular, on Tuesday we discussed the following two results in Hall's book: Corollary 2.3.2 and the first part of Theorem 4.5. On Thursday we discussed section 2.9 'The complexification of a real Lie algebra'.
Nov. 5: Ken Driessel, "Representations of SU(3)".
Abstract: We continue discussing the fifth chapter in Hall's book.
Nov. 3: Ken Driessel, "Representations of the Special Unitary Groups SU(2) and SU(3)".
Abstract: We finish discussing the fourth chapter and begin discussing the fifth chapter in Hall's book.
Oct.29: Ken Driessel, "Representations of the Special Unitary Group SU(2) and Special Orthogonal Group SO(3)".
Abstract: We continue discussing the fourth chapter in Hall's book.
Oct.27: Ken Driessel, "Schur's Lemma and Complete Reducibility".
Abstract: We continue discussing the fourth chapter in Hall's book.
Oct.22: Ken Driessel, "Basic Representation Theory ".
Abstract: We continue discussing the fourth chapter in Hall's book.
Oct.20: Ken Driessel, "Simply Connected Lie Groups and Their Representations".
Abstract: We discuss the relationship between the representations of a simply connected matrix Lie group and the representations of its Lie algebra.
Oct.15: Ken Driessel, "Basic Representation Theory".
Abstract: We begin discussing the fourth chapter in Hall's book.
Oct. 13: Ken Driessel, "Applications of the Baker-Campbell-Hausdorff Formula".
Abstract: We continue discussing the third chapter in Hall's book.
Oct. 6 and 8: Ken Driessel, "The Baker-Campbell-Hausdorff Formula".
Abstract: We continue discussing the third chapter in Hall's book.
Sept. 29 and Oct. 1: Ken Driessel, "The Baker-Campbell-Hausdorff Formula".
Abstract: We finish discussing the second chapter and begin discussing the third chapter in Hall's book.
Sept. 22 and 24: Ken Driessel, "The Lie Algebra of a Matrix Lie Group".
Abstract: We continue discussing the second chapter in Hall's book.
Sept. 15 and 17: Ken Driessel, "The Matrix Exponential and the Lie Algebra of a Matrix Lie Group".
Abstract: We begin discussing the second chapter in Hall's book.
Sept. 8 and 10: Ken Driessel, "Matrix Groups: Connectedness, Homomorphisms, Polar Decompositions".
Abstract: We continue discussing the first chapter in Hall's book.
Sept. 1 and 3: Ken Driessel, "Matrix Groups: Definition, Examples, Compactness".
Abstract: We begin discussing the first chapter in Hall's book.