Witten volume formulas for semi-simple Lie algebras
Jianqiang Zhao
TL;DR
This paper derives explicit Witten volume formulas for semi-simple Lie algebras using algebraic, combinatorial, and Dedekind sum techniques, enhancing understanding of their geometric and algebraic properties.
Contribution
It introduces a novel algebraic derivation method for Witten volume formulas, combining combinatorial approaches with Dedekind sum computations.
Findings
Explicit formulas for certain semi-simple Lie algebras
New algebraic derivation techniques demonstrated
Enhanced computational methods for Witten volumes
Abstract
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 computation of higher-dimensional Dedekind sums.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry