quantum-frobenius-canonical-basis

name	quantum-frobenius-canonical-basis
description	Quantum Frobenius morphism compatibility analysis with canonical bases. Covers imaginary vectors, tight monomial cones, and canonical basis incompatibility for finite-dimensional simple Lie algebras. Triggers: quantum Frobenius, canonical basis, imaginary vectors, tight monomial cone, Lie algebra, Leclerc vectors, quantum group, representation theory.
category	quantum-math

Quantum Frobenius Morphism and Canonical Basis Compatibility

Core Result

The quantum Frobenius morphism and its splitting are NOT fully compatible with the canonical basis for any finite-dimensional simple Lie algebra when rank is sufficiently large.

Key Connections

1. Incompatibility location: Same place where Leclerc found his imaginary vectors
2. Monomial cone issue: Monomials in the tight monomial cone which do NOT belong to the canonical basis
3. Rank dependence: Incompatibility emerges at sufficiently high rank

Applications

• Analyzing canonical basis stability under quantum Frobenius morphism
• Understanding tight monomial cone structure
• Identifying imaginary vectors in quantum group representations