Gaudin Model and Opers.
Topology of Arrangements and Applications
October 04,2004 11:00 AM to 12:00 PM
Speakers:
Frenkel, Edward
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Summary: |
This is a review of our previous works (some of them joint with B. Feigin
and N. Reshetikhin) on the Gaudin model and opers. We define a commutative
subalgebra in the tensor power of the universal enveloping algebra of a
simple Lie algebra g. This algebra includes the hamiltonians of the Gaudin
model, hence we call it the Gaudin algebra. It is constructed as a
quotient of the center of the completed enveloping algebra of the affine
Kac-Moody algebra g^ at the critical level. We identify the spectrum of
the Gaudin algebra with the space of opers associated to the Langlands
dual Lie algebra of g on the projective line with regular singularities at
the marked points. Next, we recall the construction of the eigenvectors of
the Gaudin algebra using the Wakimoto modules over g^ of critical level.
The Wakimoto modules are naturally parameterized by Miura opers (or,
equivalently, Cartan connections), and the action of the center on them is
given by the Miura transformation. |
Keywords: |
Bethe Ausatz; Vertex Algebras |
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Lecture #10696
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