Type $\hat{\mathrm C}$ Brauer loop schemes and loop model with boundaries

  title={Type \$\hat\{\mathrm C\}\$ Brauer loop schemes and loop model with boundaries},
  author={Anita K. Ponsaing and Paul Zinn-Justin},
  journal={arXiv: Mathematical Physics},
In this paper we study the Brauer loop model on a strip and the associated quantum Knizhnik--Zamolodchikov (qKZ) equation. We show that the minimal degree solution of the Brauer qKZ equation with one of four different possible boundary conditions, gives the multidegrees of the irreducible components of generalizations of the Brauer loop scheme of [Knutson--Zinn-Justin '07] with one of four kinds of symplectic-type symmetry. This is accomplished by studying these irreducible components, which… 
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