Geodesic
On the group of infinite $p$-adic matrices with integer elements
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 105-125

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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 $\mathrm{GL}$ 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. 
@article{ZNSL_2018_468_a9,
     author = {Y. A. Neretin},
     title = {On the group of infinite $p$-adic matrices with integer elements},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--125},
     publisher = {mathdoc},
     volume = {468},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a9/}
}
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Y. A. Neretin. On the group of infinite $p$-adic matrices with integer elements. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 105-125. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a9/