Ami Haviv | Searcharxiv

arXiv2002

Towards a Diagrammatic Analogue of the Reshetikhin-Turaev Link Invariants

By considering spaces of directed Jacobi diagrams, we construct a diagrammatic version of the Etingof-Kazhdan quantization of complex semisimple Lie algebras. This diagrammatic quantization is used to provide a construction of a directed version of the Kontsevich integral, denoted $Z_EK$, in a way which is analogous to the construction of the Reshetikhin-Turaev invariants from the R-matrices of the Drinfel'd-Jimbo quantum groups. Based on this analogy, we conjecture (and prove in a restricted sense) a formula for the value of the invariant $Z_EK$ on the unknot. This formula is simpler than the Wheels formula of [BGRT], but the precise relationship between the two is yet unknown.

math.QA↗

arXiv1998

The Duistermaat-Heckman Measure for the Coadjoint Orbits of Compact Semisimple Lie Groups

We apply the Guillemin-Lerman-Sternberg theorem to reprove a formula of Heckman for the Duistermaat-Heckman measure associated to the coadjoint action of $T$, a maximal torus of a compact semisimple Lie group $G$, on a regular coadjoint $G$-orbit in the dual space of the Lie algebra of $G$. This formula is, in an appropriate sense, a limiting case of the Kostant multiplicity formula.

math.SG↗