Some unitary representations of Thompson’s groups and

  • Vaughan F. R. Jones

    Vanderbilt University, Nashville, United States

Abstract

In a “naive” attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson’s groups and for any subfactor. The Thompson group elements are the “local scale transformations” of the theory. In a simple case the coefficients of the representations are polynomial invariants of links. We show that all links arise and introduce new “oriented” subgroups of and which allow us to produce all oriented knots and links.

Cite this article

Vaughan F. R. Jones, Some unitary representations of Thompson’s groups and . J. Comb. Algebra 1 (2017), no. 1, pp. 1–44

DOI 10.4171/JCA/1-1-1