Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of SU(n; n), to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses BCn symmetry and is shown to be equivalent to the standard three-parameter BCn hyperbolic Sutherland model in the cotangent bundle limit.
We construct a filtration on an integrable highest weight module of an affine Lie algebra whose adjoint graded quotient is a direct sum of global Weyl modules. We show that the graded multiplicity of each global Weyl module there is given by the corresponding level-restricted Kostka polynomial. This leads to an interpretation of level-restricted Kostka polynomials as the graded dimension of the space of conformal coinvariants. In addition, as an application of the level one case of the main result, we realize global Weyl modules of current algebras of type ADEADE in terms of Schubert subvarieties of thick affine Grassmanian, as predicted by Boris Feigin.
In 2012, Gamayun, Iorgov, and Lisovyy conjectured an explicit expression for the Painlevé VI τ function in terms of the Liouville conformal blocks with central charge c = 1. We prove that the proposed expression satisfies Painlevé VI τ function bilinear equations (and therefore prove the conjecture). The proof reduces to the proof of bilinear relations on conformal blocks. These relations were studied using the embedding of a direct sum of two Virasoro algebras into a sum of Majorana fermion and Super Virasoro algebra. In the framework of the AGT correspondence, the bilinear equations on the conformal blocks can be interpreted in terms of instanton counting on the minimal resolution of $${\mathbb{C}^2/\mathbb{Z}_2}$$C2/Z2 (similarly to Nakajima–Yoshioka blow-up equations). © 2015, Springer-Verlag Berlin Heidelberg.