Extends Lusztig total positivity to symmetric spaces G/K via Hausdorff closure, proves cell decomposition with positive parametrizations and subtraction-free transitions.
Canonical bases arising from quantum symmetric pairs
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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.
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UNVERDICTED 2representative citing papers
The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.
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Total positivity and symmetric spaces
Extends Lusztig total positivity to symmetric spaces G/K via Hausdorff closure, proves cell decomposition with positive parametrizations and subtraction-free transitions.
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The disoriented skein and iquantum Brauer categories
The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.