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The Lax operator of the Gaudin type models is a 1-form on the classicallevel. In virtue of the quantization scheme proposed in [Talalaev04](hep-th/0404153) it is natural to treat the quantum Lax operator as aconnection; this connection is a particular case of the Knizhnik-Zamolodchikovconnection [ChervovTalalaev06] (hep-th/0604128). In this paper we find a gaugetransformation which produces the "second normal form" or the"Drinfeld-Sokolov" form. Moreover the differential operator naturallycorresponding to this form is given precisely by the quantum characteristicpolynomial [Talalaev04] of the Lax operator (this operator is called the G-operor Baxter equation). This observation allows to relate solutions of the KZ andBaxter equations in an obvious way, and to prove that the immanent KZ-equationshas only meromorphic solutions. As a corollary we obtain the quantumCayley-Hamilton identity for the Gaudin-type Lax operators (including thegeneral gl(n)[t] case). The presented construction sheds a new light on ageometric Langlands correspondence. We also discuss the relation with theHarish-Chandra homomorphism.

KZ equation, G-opers, quantum Drinfeld–Sokolov reduction, and quantum Cayley–Hamilton identity