Discretized Weyl-orbit functions: modified multiplication and Galois symmetry

TL;DR

This paper explores the similarities between discretized Weyl-orbit functions and affine modular data from WZNW conformal field theories, revealing modified multiplication and Galois symmetry properties.

Contribution

It uncovers the affine fusion-like modification of orbit function multiplication and identifies Galois symmetry in discretized Weyl-orbit functions, linking them to conformal field theory structures.

Findings

Modified product of orbit functions analogous to affine fusion

Identification of Galois symmetry in discretized orbit functions

Establishment of connections between orbit functions and WZNW modular data

Abstract

We note a remarkable similarity between the discretized Weyl-orbit functions and affine modular data associated with Wess-Zumino-Novikov-Witten (WZNW) conformal field theories. Known properties of the modular data are exploited here to uncover analogous results for the discretized orbit functions. We show that the product of orbit functions is modified in analogy with the truncation of tensor products known as affine fusion, governing the interactions in WZNW models. A Galois symmetry, like that of affine modular data, is also described for the discretized orbit functions.