Geodesic
Four drafts on the representation theory of the group of infinite matrices over a~finite field
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 5-36

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The history of these drafts is described in the preface written by the first author; the drafts were written in 1997–2000, when the authors studied asymptotic representation theory. Each draft is devoted to one of the main chapters of the representation theory of the group of infinite matrices over a finite field. The list of results includes the definition of the group $GLB(q)$, which is the right analog of the group of matrices over a finite field, or a $q$-analog of the infinite symmetric group, the latter corresponding to $q=1$; a formula for the principal series characters of the group $GLB(q)$ and similar groups; the statistics of Jordan forms and a law of large numbers for the characters; a construction of simplest factor representations. 
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     title = {Four drafts on the representation theory of the group of infinite matrices over a~finite field},
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A. M. Vershik; S. V. Kerov. Four drafts on the representation theory of the group of infinite matrices over a~finite field. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 5-36. http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a0/