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,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.
| Original language | English |
|---|---|
| Pages (from-to) | 261-288 |
| Number of pages | 28 |
| Journal | Journal of Algebra |
| Volume | 664 |
| Issue number | B |
| DOIs | |
| Publication status | Published - 15 Feb 2025 |
Bibliographical note
Funding Information:The work of K.DC. and S.T.M. was supported by the FWO grants G025115N and G032919N. S.T.M. was additionally supported by Narodowe Centrum Nauki, grant number 2017/26/A/ST1/00189.
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