Canonical bases arising from $ı$quantum covering groups

Abstract

For $ı$quantum covering groups $(\mathbf{U},{\mathbf{U}}^{ı})$ of super Kac-Moody type, we construct $ı$-canonical bases for the highest weight integrable $\mathbf{U}$-modules and their tensor products regarded as ${\mathbf{U}}^{ı}$-modules, as well as a canonical basis for the modified form of the $ı$quantum group ${\mathbf{U}}^{ı}$, using the ${ı}^{\pi }$-divided powers, rank one canonical basis for ${\mathbf{U}}^{ı}$.

arXiv comment29 pages including references

References in corpus (15)

• Quantum symmetric Kac-Moody pairs
• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Canonical bases for tensor products and super Kazhdan-Lusztig theory
• The bar involution for quantum symmetric pairs
• Geometric Schur duality of classical type
• Canonical bases arising from quantum symmetric pairs of Kac-Moody type
• Super Kac-Moody 2-categories
• A Serre presentation for the $ı$quantum groups
• Kazhdan-Lusztig Theory of super type D and quantum symmetric pairs
• Formulae of $ı$-divided powers in ${\mathbf{U}}_q({\mathfrak{sl}}_2)$
• Positivity vs negativity of canonical bases
• DG structures on odd categorified quantum sl(2)
• Formulae of $ı$-divided powers in ${\mathbf{U}}_q({\mathfrak{sl}}_2)$, II
• Canonical bases for the quantum enveloping algebra of gl(m|1) and its modules
• A Serre presentation for the $ı$quantum covering groups