预投射代数的量子化与A型有理Cherednik代数
Quantization of Preprojective Algebras and the Type A Rational Cherednik Algebra
- School of Mathematics, Sichuan University（四川大学数学学院）
- School of Mathematics and Statistics, Hainan University（海南大学数学与统计学院）
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中文总结 AI 辅助
本文构造Jordan箭图的量子预投射代数到不变微分算子代数的径向量子迹态射，证明其满射性，并建立与非交换量子化及A型球面有理Cherednik代数的联系，给出Harish-Chandra同态的显式公式。
中文摘要 AI 辅助
对于Jordan箭图，我们构造了一个从量子预投射代数到Cartan子代数上不变微分算子代数的径向量子迹态射。其经典极限恢复了与交换商相关的经典迹态射，并且我们证明了量子迹态射和经典迹态射都是满射。我们进一步将Jordan预投射代数的非交换量子化与A型球面有理Cherednik代数联系起来。最后，我们在幂和坐标中推导出Harish-Chandra同态及其径向部分的显式公式。
英文摘要
For the Jordan quiver, we construct a radial quantum trace morphism from the quantum preprojective algebra to the algebra of invariant differential operators on the Cartan subalgebra. Its classical limit recovers the classical trace morphism associated with the commuting quotient, and we prove that both the quantum and classical trace morphisms are surjective. We further relate noncommutative quantizations of the Jordan preprojective algebra to the spherical rational Cherednik algebra of type A. Finally, we derive explicit formulas for the Harish--Chandra homomorphism and its radial part in power-sum coordinates.
