4 research outputs found
A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories
We give an explicit differential equation which is expected to determine the
instanton partition function in the presence of the full surface operator in
N=2 SU(N) gauge theory. The differential equation arises as a quantization of a
certain Hamiltonian system of isomonodromy type discovered by Fuji, Suzuki and
Tsuda.Comment: 15 pages, v2: typos corrected and references added, v3: discussion,
appendix and references adde
Spaces of quasi-exponentials and representations of gl_N
We consider the action of the Bethe algebra B_K on (\otimes_{s=1}^k
L_{\lambda^{(s)}})_\lambda, the weight subspace of weight of the
tensor product of k polynomial irreducible gl_N-modules with highest weights
\lambda^{(1)},...,\lambda^{(k)}, respectively. The Bethe algebra depends on N
complex numbers K=(K_1,...,K_N). Under the assumption that K_1,...,K_N are
distinct, we prove that the image of B_K in the endomorphisms of
(\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic to the algebra of
functions on the intersection of k suitable Schubert cycles in the Grassmannian
of N-dimensional spaces of quasi-exponentials with exponents K. We also prove
that the B_K-module (\otimes_{s=1}^k L_{\lambda^{(s)}})_\lambda is isomorphic
to the coregular representation of that algebra of functions. We present a
Bethe ansatz construction identifying the eigenvectors of the Bethe algebra
with points of that intersection of Schubert cycles.Comment: Latex, 29 page