Littlewood-Richardson rule for generalized Schur Q-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 Schur Q-functions is also given as the combinatorial model by using the shifted tableaux. In this paper, we firstly use the shifted Littlewood-Richardson coefficients to give the coefficients of generalized Schur Q-function expanded as a sum of Schur Q-functions and the structure constants for the multiplication of two generalized Schur Q-functions, respectively. Then we will combine the vertex operator realizations of generalized Schur Q-functions and raising operators to construct the algebraic forms for the multiplication of generalized Schur Q-functions.