Canonical bases in tensor products revisited

We construct canonical bases in tensor products of several lowest and highest weight integrable modules, generalizing Lusztig's work.Comment: 7 pages, v2, improved exposition, one reference added, to appear in Amer. J. Mat

Canonical bases arising from quantum symmetric pairs

We develop a general theory of canonical bases for quantum symmetric pairs (\mathbf{U}, \mathbf{U}^\imath) with parameters of arbitrary finite type. We construct new canonical bases for the simple integrable $\mathbf{U}$-modules and their tensor products regarded as \mathbf{U}^\imath-modules. We also construct a canonical basis for the modified form of the $\imath$quantum group \mathbf{U}^\imath. To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank one), and integrality of the intertwiners.Comment: v1, 76 pages. v2, 62 pages, much shortened appendix, modified introduction and other corrections, to appear in Invent. Mat

Cooperative order and excitation spectra in the bicomponent spin networks

A ferrimagnetic spin model composed of $S=1/2$ spin-dimers and $S=5/2$ spin-chains is studied by combining the bond-operator representation (for $S=1/2$ spin-dimers) and Holstein-Primakoff transformation (for $S=5/2$ spins). A finite interaction $J_{\rm DF}$ between the spin-dimer and the spin chain makes the spin chains ordered antiferromagnetically and the spin dimers polarized. The effective interaction between the spin chains, mediated by the spin dimers, is calculated up to the third order. The staggered magnetization in the spin dimer is shown proportional to $J_{\rm DF}$. It presents an effective staggered field reacting on the spin chains. The degeneracy of the triplons is lifted due to the chain magnetization and a mode with longitudinal polarization is identified. Due to the triplon-magnon interaction, the hybridized triplon-like excitations show different behaviors near the vanishing $J_{\rm DF}$. On the other hand, the hybridized magnon-like excitations open a gap $\Delta_A\sim J_{\rm DF}$. These results consist well with the experiments on Cu$_{2}$Fe$_{2}$Ge$_{4}$O$_{13}$.Comment: 7 pages, 5 figure