On Universal Quantum Dimensions

Abstract

We represent in the universal form restricted one-instanton partition function of supersymmetric Yang-Mills theory. It is based on the derivation of universal expressions for quantum dimensions (universal characters) of Cartan powers of adjoint and some other series of irreps of simple Lie algebras. These formulae also provide a proof of formulae for universal quantum dimensions for low-dimensional representations, needed in derivation of universal knot polynomials (i.e. colored Wilson averages of Chern-Simons theory on 3d sphere). As a check of the (complicated) formulae for universal quantum dimensions we prove numerically Deligne's hypothesis on universal characters for symmetric cube of adjoint representation.

11 pages, Wording improved, Table 4 simplified

References in corpus (4)

• Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots
• On universal knot polynomials
• Universal volume of groups and anomaly of Vogel's symmetry
• Diophantine equations, Platonic solids, McKay correspondence, equivelar maps and Vogel's universality

Cited by in corpus (9)

• Macdonald deformation of Vogel's universality and link hyperpolynomials
• On Refined Vogel's universality
• On Universal Eigenvalues of Casimir Operator
• $X_2$ series of universal quantum dimensions
• Vogel's universality and Macdonald dimensions
• Torus knots in adjoint representation and Vogel's universality
• Vogel's universality and the classification problem for Jacobi identities
• On universal quantum dimensions of certain two-parameter series of representations
• Universal quantum dimensions: $\gamma$-dependent factors