Symmetry classes of polynomials associated with the ‎direct ‎product of permutation groups

Document Type: Research Paper

Authors

1 Sahand University of technology

2 Sahand University of Technology

Abstract

‎Let $G_{i} $ be a subgroup of $ S_{m_{i}}‎ ,‎\ 1 \leq i \leq k$‎. ‎Suppose $\chi_{i}$ is an irreducible complex character of $G_{i}$‎. ‎We consider $ G_{1}\times \cdots \times G_{k} $ as subgroup of $ S_{m} $‎, ‎where $ m=m_{1}+\cdots‎ +‎m_{k} $‎. ‎In this paper‎, ‎we give a formula for the dimension of $H_{d}(G_{1}\times \cdots \times G_{k}‎, ‎\chi_{1}\times\cdots \times \chi_{k})$ and investigate the existence of an o-basis of this type of classes‎.

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