Verlinde formula

In mathematics, a Verlinde algebra is a finite-dimensional associative algebra introduced by Erik Verlinde (1988), with a basis of elements φ_λ corresponding to primary fields of a two-dimensional rational conformal field theory, whose structure constants Nν
λμ describe fusion of primary fields.

In terms of the modular modular group S-matrix

${\displaystyle N_{\lambda \mu }^{\nu }=\sum _{\sigma }{\frac {S_{\lambda \sigma }S_{\mu \sigma }{\bar {S_{\nu \sigma }}}}{S_{0\sigma }}}}$

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 Freed, Hopkins and Teleman (2001) showed that the Verlinde algebra can be identified with twisted equivariant K-theory of G.

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