Vertex Operators, Littlewood-Richardson Rule for Generalized Symplectic Schur Functions

Littlewood-Richardson rule gives the expansion formula for decomposing a product of two Schur functions as a linear sum of Schur functions,while the decomposition formula for the multiplication of two symplectic Schur function is also given by the combinatorial method.In this paper,we will construct the algebraic forms of the decomposition formula for the product of two symplectic Schur functions by using the generating functions and vertex operator realizations,and then extend these results to generalized symplectic Schur functions.

NH_(3,6)中的李特尔伍德-理查德森系数

构造出分圆幂零赫克代数NH_(3,6)所有的基本子代数基,将这组基里的元素一一对应到格拉斯曼流形的舒本特类。计算了在这组基下的乘法结构常数,验证了这些结构常数与G(3,6)中舒本特类相交所生成的李特尔伍德数是完全一致的,并通过该一一对应证明了基本子代数和特殊上同调代数是完全同构的结论。