Positivity of Canonical Bases under Comultiplication

Abstract

We show the positivity of the canonical basis for a modified quantum affine ${\mathfrak{sl}}_n$ under the comultiplication. Moreover, we establish the positivity of the i-canonical basis in [LW15] with respect to the coideal subalgebra structure.

46 pages

References in corpus (3)

• A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs
• Geometric Schur duality of classical type
• Quantum affine ${\mathfrak{gl}}_n$ via Hecke algebras

Cited by in corpus (7)

• Affine flag varieties and quantum symmetric pairs
• Positivity vs negativity of canonical bases
• Affine flag varieties and quantum symmetric pairs, II. Multiplication formula
• Canonical bases arising from quantum symmetric pairs
• Multiplicaton formulas and canonical basis for quantum affine gl_n
• On canonical bases of Letzter algebra ${\mathbf{U}}^{ı}({\mathfrak{sl}}_2)$
• Positivity of $ı$-canonical bases