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arXiv · 2303.10749

On Symmetrizers in Quantum Matrix Algebras

Dmitry Gurevich·Pavel Saponov·Vladimir Sokolov
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Abstract

In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions on classical Lie groups (the RTT algebras). We consider the problem of constructing some projectors on homogenous components of such algebras, which are analogs of the usual symmetrizers. The main objective of this note is to present a method, which hopefully enables one to construct symmetrizers on all homogenous components of the RTT algebras. We illustrate the construction by two low-dimensional examples. A way of extending this method onto other quantum matrix algebras is also discussed.

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BibTeXRIS

Dmitry Gurevich, Pavel Saponov, Vladimir Sokolov. 2023-03-19. On Symmetrizers in Quantum Matrix Algebras. https://arxiv.org/abs/2303.10749

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