Abstract
We consider a pair of a compact quantum group and a coideal in its dual Hopf *-algebra and introduce the notions of Gelfand pair and strict Gelfand pair. For a strict Gelfand pair, we construct two hyper-complex systems dual to each other. As an example, we consider the quantum analog of the pair (U(n), SO(n)).
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 8, pp. 1055–1066, August, 1994.
This research was partially supported by the Foundation for Fundamental Researches of the Ukrainian State Committee on Science and Technology (Project 1/238 “Operator”).
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Chapovskii, Y.A. Gelfand pair associated with a hoph algebra and a coideal. Ukr Math J 46, 1157–1171 (1994). https://doi.org/10.1007/BF01056176
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DOI: https://doi.org/10.1007/BF01056176