Littlewood-Richardson rule for generalized Schur Q-functions. (English) Zbl 07788003
Summary: 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.
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 05E05 | Symmetric functions and generalizations |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 20G43 | Schur and \(q\)-Schur algebras |
Keywords:
Littlewood-Richardson rule; vertex operators; Schur Q-functions; generalized Schur Q-functions; structure constantsReferences:
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