Let k be an algebraically closed field and O = k[[t]] ⊂ F = k((t)). For an almost simple algebraic group G we classify central extensions 1 → $\mathbb{G}_m\to E\to G(\bm{F})\$m → E → G(F) → 1; any such extension splits canonically over G(O). Fix a positive integer N and a primitive character ζ : μN(K) →$\mathbb{Q}}_\ell^*}$ (under some assumption o...

Twisted geometric Satake equivalence

10.1017/S1474748010000034