ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV

Witten Volume Formulas for Semi-simple Lie Algebras

In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in the computation of higher-dimensional Dedekind sums.

Reduced zeta functions of Lie algebras

We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to analyse. We prove that reduced zeta functions are multiplicative under certain conditions and investigate which reduced zeta functions have functional equations.

On Cachazo–Douglas–Seiberg–Witten Conjecture for Simple Lie Algebras

Let g be a finite dimensional simple Lie algebra over the complex numbers C. Consider the exterior algebra R := ∧ (g⊕ g) on two copies of g. Then, the algebra R is bigraded under R = ∧p(g)⊗∧q(g). The diagonal adjoint action of g gives rise to a g-algebra structure on R compatible with the bigrading. There are three ‘standard’ copies of the adjoint representation g in R. Let J be the (bigraded) ...

Semi-simple Lie Algebras and Their Representations

This paper presents an overview of the representations of Lie algebras, particularly semi-simple Lie algebras, with a view towards theoretical physics. We proceed from the relationship between Lie algebras and Lie groups to more abstract characterizations of Lie groups, give basic definitions of different properties that may characterize Lie groups, and then prove results about root systems, pr...

Semi-Simple Lie Algebras and Their Representations