Title: Decomposition of a rank 3 hyperbolic Kac-Moody algebra with respect to the hyperbolic Fibonacci KM subalgebra
Speaker: Diego Penta (Ohio State University)
Abstract: In 1983, Feingold-Frenkel found important structural results about the rank 3 hyperbolic Kac-Moody Lie algebra F from its decomposition with respect to the affine subalgebra $A_1^{(1)}$. In this talk, we will discuss an alternative decomposition of F with respect to the rank 2 hyperbolic KM algebra Fib, the so-called `Fibonacci' algebra (Feingold, 1980). We find that F has a grading by Fib-level, and show that each graded piece Fib(m) is an integrable Fib-module which contains infinitely many irreducible components. We also discuss the existence of non-standard modules on levels |m| less than 3, whose weight multiplicities do not appear to satisfy the recursion formulas given by Racah-Speiser and Kac-Peterson.
Seminar URL: https://research.math.osu.edu/reps/
