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Edward Frenkel (together with Boris Feigin and others) has proven many interesting results connecting the representation theory of an affine Kac-Moody algebra at the critical level with the geometry ...

For a simple Lie algebra $\mathfrak{g}$, we have the W-algebra of level $k$, denoted by $\mathcal{W}^k(\mathfrak{g})$. Using Wakimoto free field realization and screening operators, Feigin and Frenkel ...