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$ν λμ$ describe fusion of primary fields.

Verlinde formula
In terms of the modular S-matrix, the fusion coefficients are given by

$$ N_{\lambda \mu}^\nu = \sum_\sigma \frac{S_{\lambda \sigma} S_{\mu \sigma} S^*_{\sigma \nu}}{S_{0\sigma}} $$

where $$ S^* $$ is the component-wise complex conjugate of $$ S $$.

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.