  The Lax operator of the Gaudin type models is a 1-form on the classical
level. In virtue of the quantization scheme proposed in [Talalaev04]
(hep-th/0404153) it is natural to treat the quantum Lax operator as a
connection; this connection is a particular case of the Knizhnik-Zamolodchikov
connection [ChervovTalalaev06] (hep-th/0604128). In this paper we find a gauge
transformation which produces the "second normal form" or the
"Drinfeld-Sokolov" form. Moreover the differential operator naturally
corresponding to this form is given precisely by the quantum characteristic
polynomial [Talalaev04] of the Lax operator (this operator is called the G-oper
or Baxter equation). This observation allows to relate solutions of the KZ and
Baxter equations in an obvious way, and to prove that the immanent KZ-equations
has only meromorphic solutions. As a corollary we obtain the quantum
Cayley-Hamilton identity for the Gaudin-type Lax operators (including the
general gl(n)[t] case). The presented construction sheds a new light on a
geometric Langlands correspondence. We also discuss the relation with the
Harish-Chandra homomorphism.
