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

@article{Ponsaing2014TypeC, 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}, year={2014} }

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…

## 3 Citations

### Bethe subalgebras in affine Birman–Murakami–Wenzl algebras and flat connections for q-KZ equations

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Commutative sets of Jucys–Murphy elements for affine braid groups of A ( 1 ) , B ( 1 ) , C ( 1 ) , D ( 1 ) types were defined. Construction of R-matrix representations of the affine braid group of…

### The dilute Temperley–Lieb O(n = 1) loop model on a semi infinite strip: the sum rule

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This is the second part of our study of the ground state eigenvector of the transfer matrix of the dilute Temperley–Lieb loop model with the loop weight n = 1 on a semi infinite strip of width L…

### Quiver varieties and the quantum Knizhnik–Zamolodchikov equation

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We show how equivariant volumes of tensor product quiver varieties of type A are given by matrix elements of vertex operators of centrally extended doubles of Yangians and how these elements satisfy…

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