The Haar state of O(SL_q(3)) on a monomial basis

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• Ting Lu (Harbin Institute of Technology)
• Thursday 05 December 2024, 14:10-14:30
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

The Haar measure of compact Lie groups plays an important role in the representation theory and many other aspects of Lie groups. On O(SL_q(3)), the quantized algebra of coordinate function of SL(3), there is a q-deformed Haar measure called the Haar state. Since O(SL_q(3)) is a cosemisimple Hopf-* algebra, the Haar state of O(SL_q(3)) is determined by its Peter-Weyl decomposition. However, the explicit expressions of the matrix coefficients are still unclear and evaluating the Haar state using matrix coefficeints is inefficient. In this talk, we define a monomial basis on O(SL_q(3)) and give the explicit expressions of the Haar states of these monomials as rational polynomials in variable q. Then, we will briefly discuss the methods used in the computation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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