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The group of type is a coideal subalgebra of the quantum group , associated with the symmetric pair . In this paper, we give a cluster realisation of the algebra . Under such a realisation, we give cluster interpretations of some fundamental constructions of , including braid group symmetries, the coideal structure and the action of a Coxeter eleme...
We prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialization, we deduce that the canonical Frobenius splittings on flag varieties are compatible with cluster algebra structures on Schubert cells.
We prove that the duals of the quantum Frobenius morphisms and their splittings by Lusztig are compatible with quantum cluster monomials. After specialisation, we deduce that the canonical Frobenius splittings on flag varieties are compatible with cluster algebra structures on Schubert cells.
Let $G_k$ be a connected reductive algebraic group over an algebraically closed field $k$ of characteristic $\neq 2$. Let $K_k \subset G_k$ be a quasi-split symmetric subgroup of $G_k$ with respect to an involution $\theta_k$ of $G_k$. The classification of such involutions is independent of the characteristic of $k$ (provided not $2$). We first co...