Witten Volume Formulas for Semi-simple Lie Algebras

A simple way to compute structure constants

The standard technique for computing the structure constants of semi-simple Lie algebras is used in the computer program MAGMA and described by [Cohen-Murray-Taylor:2005]. It relies on the additive structure of roots. In [Casselman:2015] I explained a reasonably efficient way to compute the structure constants of semi-simple Lie algebras by implementing an idea originally found in [Tits:1966a]....

Second order reductions of the WDVV Equations related to classical Lie algebras

We construct second order reductions of the generalized Witten-DijkgraafVerlinde-Verlinde system based on simple Lie algebras. We discuss to what extent some of the symmetries of the WDVV system are preserved by the reduction. MSC Subj. Class. 2000: 35C05, 81T60

Series of Lie Groups

For various series of complex semi-simple Lie algebras g(t) equipped with irreducible representations V (t), we decompose the tensor powers of V (t) into irreducible factors in a uniform manner, using a tool we call diagram induction. In particular, we interpret the decompostion formulas of Deligne [4] and Vogel [23] for decomposing g respectively for the exceptional series and k ≤ 4 and all si...

On the Cachazo-douglas-seiberg-witten Conjecture for Simple Lie Algebras

Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z2-graded Lie algebras

We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of certain abelian subalgebras of simple Lie algebras.