# $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$-invariant non-compact boundary conditions for the XXZ spin chain

@article{Chernyak2022, title={\$\$ \{U\}\_\{\mathfrak\{q\}\}\{\mathfrak\{sl\}\}\_2 \$\$-invariant non-compact boundary conditions for the XXZ spin chain}, author={Dmitry Chernyak and Azat M. Gainutdinov and H. Saleur}, journal={Journal of High Energy Physics}, year={2022} }

Abstract
We introduce new $$ {U}_{\mathfrak{q}}{\mathfrak{sl}}_2 $$
U
q
sl
2
-invariant boundary conditions for the open XXZ spin chain. For generic values of $$ \mathfrak{q} $$
q
we couple the bulk Hamiltonian to an infinite-dimensional Verma module on one or both boundaries of the spin chain, and for $$ \mathfrak{q}={e}^{\frac{i\pi}{p}} $$
q
=
e
iπ
p
a 2p-th root of unity — to its p-dimensional analogue. Both cases are parametrised by a continuous “spin” α ∈ ℂ.To…

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