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arXiv · 2407.03613

Representation theory of the Reflection Equation Algebra II: Theory of shapes

Kenny De Commer·Stephen T. Moore
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Abstract

We continue our study of the representations of the Reflection Equation Algebra (=REA) on Hilbert spaces, focusing again on the REA constructed from the $R$-matrix associated to the standard $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We consider the Poisson structure appearing as the classical limit of the $R$-matrix, and parametrize the symplectic leaves explicitly in terms of a type of matrix we call a shape matrix. We then introduce a quantized version of the shape matrix for the REA, and show that each irreducible representation of the REA has a unique shape.

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Kenny De Commer, Stephen T. Moore. 2024-07-04. Representation theory of the Reflection Equation Algebra II: Theory of shapes. https://arxiv.org/abs/2407.03613

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