Let G be an infinite-dimensional real classical group containing the complete unitary group (or the complete orthogonal group) as a subgroup. Then G generates a category of double cosets (train), and any unitary representation of G can be canonically extended to the train. We prove a technical lemma on the complete group GL of infinite p-adic matrices with integer coefficients; this lemma implies that the phenomenon of an automatic extension of unitary representations to a train is valid for infinite-dimensional p-adic groups.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 468, 2018, pp. 105–125.
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Neretin, Y.A. On the Group of Infinite p-Adic Matrices with Integer Elements. J Math Sci 240, 572–586 (2019). https://doi.org/10.1007/s10958-019-04376-w
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DOI: https://doi.org/10.1007/s10958-019-04376-w