对称和反对称向量值Jack多项式
Symmetric and Antisymmetric Vector-valued Jack Polynomials
摘要：
值在对称群的不可约模中的多项式可以给出有理切雷德尼克代数的模的结构，称为标准模。这个代数有一个自由参数，由微分-差分（“Dunkl”）算子、乘坐标函数和群代数生成。通过将Griffeth（arXiv：0707.0251）的结果特殊化为G（r，p，n）的情形，得到了标准模中对称和反对称多项式的范数公式。这样的多项式的最低程度的规范，其中涉及钩长和推广的交替多项式的规范。
英文摘要：
Polynomials with values in an irreducible module of the symmetric group can be given the structure of a module for the rational Cherednik algebra, called a standard module. This algebra has one free parameter and is generated by differential-difference ("Dunkl") operators, multiplication by coordinate functions and the group algebra. By specializing Griffeth's (arXiv:0707.0251) results for the G(r,p,n) setting, one obtains norm formulae for symmetric and antisymmetric polynomials in the standard module. Such polynomials of minimum degree have norms which involve hook-lengths and generalize the norm of the alternating polynomial.
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