Canonical bases in Lie theory and total positivity
G. Lusztig
TL;DR
This paper reviews the theory of canonical bases in quantum groups and explores their connection with total positivity, highlighting recent developments in Lie theory.
Contribution
It provides a comprehensive overview of canonical bases and their relation to total positivity, emphasizing new insights in Lie theory.
Findings
Canonical bases are fundamental in quantum groups.
Total positivity relates closely to canonical bases.
Recent advances connect these areas in Lie theory.
Abstract
This represents a talk given at the International Conference for Basic Science, July 2025. We review the theory of canonical bases of quantum groups and its relation with the theory of total positivity.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research · Noncommutative and Quantum Gravity Theories