The matrix-extended $W_{1+\infty}$ algebra
High Energy Physics - Theory
2019-10-18 v1 Mathematical Physics
math.MP
Representation Theory
Abstract
We construct a quadratic basis of generators of matrix-extended using a generalization of the Miura transformation. This makes it possible to conjecture a closed-form formula for the operator product expansions defining the algebra. We study truncations of the algebra. An explicit calculation at low levels shows that these are parametrized in a way consistent with the gluing description of the algebra. It is perhaps surprising that in spite of the fact that the algebras are rather complicated and non-linear, the structure of their truncations follows very simple gluing rules.
Cite
@article{arxiv.1910.00041,
title = {The matrix-extended $W_{1+\infty}$ algebra},
author = {Lorenz Eberhardt and Tomáš Procházka},
journal= {arXiv preprint arXiv:1910.00041},
year = {2019}
}