Verlinde algebra

In mathematics, a Verlinde algebra is a finite-dimensional associative algebra introduced by , with a basis of elements φλ corresponding to primary fields of a rational two-dimensional conformal field theory, whose structure constants "N" describe fusion of primary fields.
Verlinde formula.
In terms of the modular S-matrix, the fusion coefficients are given by
formula_1
where formula_2 is the component-wise complex conjugate of formula_3.
Twisted equivariant K-theory.
If "G" is a compact Lie group, there is a rational conformal field theory whose primary fields correspond to the representations λ of some fixed level of loop group of "G". For this special case showed that the Verlinde algebra can be identified with twisted equivariant K-theory of "G".