Mathematics – Group Theory
Scientific paper
2003-09-14
Mathematics
Group Theory
44 pages, plain tex
Scientific paper
If $\frak g$ is a complex simple Lie algebra, and $k$ does not exceed the dual Coxeter number of $\frak g$, then the k$^{th}$ coefficient of the $dim \frak g$ power of the Euler product may be given by the dimension of a subspace of $\wedge^k\frak g$ defined by all abelian subalgebras of $\frak g$ of dimension $k$. This has implications for all the coefficients of all the powers of the Euler product. Involved in the main results are Dale Peterson's $2^{rank}$ theorem on the number of abelian ideals in a Borel subalgebra of $\frak g$, an element of type $\rho$ and my heat kernel formulation of Macdonald's $\eta$-function theorem, a set $D_{alcove}$ of special highest weights parameterized by all the alcoves in a Weyl chamber (generalizing Young diagrams of null $m$-core when $\frak g= Lie Sl(m,\Bbb C)$), and the homology and cohomology of the nil radical of the standard maximal parabolic subalgebra of the affine Kac-Moody Lie algebra.
No associations
LandOfFree
Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Powers of the Euler product and commutative subalgebras of a complex simple Lie algebra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-161028