Hook fusion procedure for direct product of symmetric groups

Dimpi KM; Geetha Thangavelu

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arXiv · 2504.01417

Hook fusion procedure for direct product of symmetric groups

Dimpi KM·Geetha Thangavelu

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Abstract

In this work, we derive a new expression for the diagonal matrix elements of irreducible representations of the direct product group $S_r\times S_s$ using Grime's hook fusion procedure for symmetric groups, which simplifies the fusion procedure by reducing the number of auxiliary parameters needed. By extending this approach to the product group setting, we provide a method for constructing a complete set of orthogonal primitive idempotents.

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Dimpi KM, Geetha Thangavelu. 2025-04-02. Hook fusion procedure for direct product of symmetric groups. https://arxiv.org/abs/2504.01417

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