$A_N$李代数的非递归重数公式
Non-Recursive Multiplicity Formulas for $A_N$ Lie Algebras
摘要：
证明了$A_N$李代数不可约表示中权重数的计算公式有无穷多个。相反，递归字符的Kostant和Freudenthal的多重性公式，他们为我们提供了系统的线性代数方程组与N-依赖多项式系数。这些多项式系数实际上与表示Casimir算子特征值的多项式有关。
英文摘要：
It is shown that there are infinitely many formulas to calculate multiplicities of weights participating in irreducible representations of $A_N$ Lie algebras. On contrary to recursive character of Kostant and Freudenthal multiplicity formulas, they provide us systems of linear algebraic equations with N-dependent polinomial coefficients. These polinomial coefficients are in fact related with polinomials which represent eigenvalues of Casimir operators.
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