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Littlewood-Richardson rule for generalized Schur Q-functions

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Abstract

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.

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Acknowledgements

Chuanzhong Li is supported by the National Natural Science Foundation of China under Grant No. 12071237.

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Authors and Affiliations

  1. School of mathematics and statistics, Henan University, Kaifeng, 475004, China

    Fang Huang & Yanjun Chu

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Chuanzhong Li

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  1. Fang Huang
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  2. Yanjun Chu
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Huang, F., Chu, Y. & Li, C. Littlewood-Richardson rule for generalized Schur Q-functions. Algebr Represent Theor 26, 3143–3165 (2023). https://doi.org/10.1007/s10468-023-10204-2

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