整体晶体基（又称为典范基）在量子群及其表示理论中起着重要的作用。
The global crystal basis or canonical basis plays an important role in the theory of the quantum groups and their representations.
从那时开始，人们发现量子群在很多领域都有着深刻的应用，范围遍及理论物理、辛几何、扭结理论与约化代数群的模表示理论等。
Since then they have found numerous and deep applications in areas ranging from theoretical physics, symplectic geometry, knot theory, and modular representations of reductive algebraic groups.
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