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arXiv · 1504.01241

Gram Matrices and Stirling numbers of a class of Diagram Algebras

N. Karimilla Bi·M. Parvathi
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Abstract

In this paper, we introduce Gram matrices for the signed partition algebras, the algebra of $\mathbb{Z}_2$-relations and the partition algebras. We prove that the Gram matrix is similar to a matrix which is a direct sum of block submatrices. In this connection, $(s_1, s_2, r_1, r_2, p_1, p_2)$-Stirling numbers of the second kind are introduced and their identities are established. As a consequence, the semisimplicity of a signed partition algebra is established.

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BibTeXRIS

N. Karimilla Bi, M. Parvathi. 2015-04-06. Gram Matrices and Stirling numbers of a class of Diagram Algebras. https://arxiv.org/abs/1504.01241

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