Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8966097 | Journal of Algebra | 2018 | 25 Pages |
Abstract
We give formulae for the multiplicities of eigenvalues of generalized rotation operators in terms of generalized Frobenius-Schur indicators in a semisimple spherical tensor category C. In particular, this implies that the entire collection of rotation eigenvalues for a fusion category can be computed from the fusion rules and the traces of rotation at finitely many tensor powers. We also establish a rigidity property for FS indicators of fusion categories with a given fusion ring via Jones's theory of planar algebras. If C is also braided, these formulae yield the multiplicities of eigenvalues for a large class of braids in the associated braid group representations. When C is modular, this allows one to determine the eigenvalues and multiplicities of braids in terms of just the S and T matrices.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Daniel Barter, Corey Jones, Henry Tucker,