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Published in:
2014 | OriginalPaper | Chapter
Critical Points of Master Functions and the mKdV Hierarchy of Type A 2 (2)
Authors : A. Varchenko, T. Woodruff, D. Wright
Published in: Bridging Algebra, Geometry, and Topology
Publisher: Springer International Publishing
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Abstract
We consider the population of critical points generated from the critical point of the master function with no variables, which is associated with the trivial representation of the affine Lie algebra A
2
(2). The population consists of a sequence of m-parameter families of critical points, where \(m = 0,1,\ldots\). We embed such a family into the space \(\mathcal{M}(A_{2}^{(2)})\) of Miura opers of type A
2
(2). We show that the embedding defines a variety which is invariant with respect to all mKdV flows on \(\mathcal{M}(A_{2}^{(2)})\), and that variety is point-wise fixed by all flows of the index big enough.