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arXiv · 2404.01493

Schur-Weyl dualities for the rook monoid: an approach via Schur algebras

Carlos A. M. André·Inês Legatheaux Martins
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Abstract

The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure when it comes to extend the principle of symmetry. In this paper, we establish a Schur-Weyl duality between this monoid and an extension of the classical Schur algebra, which we name the extended Schur algebra. We also explain how this relates to Solomon's Schur-Weyl duality between the rook monoid and the general linear group and mention some advantages of our approach.

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Carlos A. M. André, Inês Legatheaux Martins. 2024-04-01. Schur-Weyl dualities for the rook monoid: an approach via Schur algebras. https://arxiv.org/abs/2404.01493

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