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arXiv · 1504.01377

Eigenvalues of Gram Matrices of a class of Diagram Algebras

N. Karimilla Bi·M. Parvathi
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Abstract

In this paper, we introduce symmetric diagram matrices $A_{s+r,s}$ of size ${_{(s+r)}}C_s$ whose entries are $\{x_i\}_{min\{s,r\}}$. We compute the eigenvalues of symmetric diagram matrices using elementary row and column operations inductively. As a byproduct, we obtain the eigenvalues of Gram matrices of a larger class of diagram algebras like the signed partition algebras, algebra of $\mathbb{Z}_2$ relations and partition algebras.

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N. Karimilla Bi, M. Parvathi. 2015-04-06. Eigenvalues of Gram Matrices of a class of Diagram Algebras. https://arxiv.org/abs/1504.01377

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