Geodesic
Tame representations of the group~GL(∞,Fq)
Algebra i analiz, Tome 18 (2006) no. 2, pp. 57-79.

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A complete classification of irreducible tame representations of the group G(∞)=lim→⁡G(n) is presented. Here G(n)=GL(n,Fq) is the group of nonsingular matrices of order n over the finite field Fq. 
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A. V. Dudko. Tame representations of the group~$\mathrm{GL}(\infty,\mathbb F_q)$. Algebra i analiz, Tome 18 (2006) no. 2, pp. 57-79. https://geodesic-test.mathdoc.fr/item/AA_2006_18_2_a2/

[1] Kirillov A. A., Elementy teorii predstavlenii, Nauka, M., 1978 | MR | Zbl

[2] Okunkov A. Yu., “Teorema Toma i predstavleniya beskonechnoi bisimmetricheskoi gruppy”, Funkts. anal. i ego pril., 28:2 (1994), 31–40 | DOI | MR | Zbl

[3] Okunkov A. Yu., “O predstavleniyakh beskonechnoi simmetricheskoi gruppy”, Zap. nauch. semin. POMI, 240, 1997, 166–228 ; arXiv: math. RT/9803037 | MR | Zbl

[4] Ol'shanskiĭ G. I., “Unitary representations of the infinite symmetric group: a semigroup approach”, Representations of Lie Groups and Lie Algebras (Budapest, 1971), Acad. Kiado, Budapest, 1985, 181–197 | MR

[5] Olshanskii G. I., “Unitarnye predstavleniya $(G,K)$-par, svyazannykh s beskonechnoi simmetricheskoi gruppoi $S(\infty)$”, Algebra i analiz, 1:4 (1989), 178–209 | MR | Zbl

[6] Ol'shanskiĭ G. I., “On semigroups related to infinite-dimensional groups”, Topics in Representation Theory, Adv. Soviet Math., 2, Amer. Math. Soc., Providence, RI, 1991, 67–101 | MR

[7] Olshanskii G. I., “Novye «bolshie» gruppy tipa I”, Itogi nauki i tekhn. Sovrem. probl. mat., 16, VINITI, M., 1980, 31–52 | MR | Zbl

[8] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR

[9] Neretin Yu. A., Kategorii simmetrii i beskonechnomernye gruppy, Editorial URSS, 1998

[10] Saito M., “Représentations unitaires monomiales d'un groupe discret, en particulier du groupe modulaire”, J. Math. Soc. Japan, 26:3 (1974), 464–482 | DOI | MR | Zbl

[11] Ismagilov R. S., “O lineinykh predstavleniyakh grupp matrits s elementami iz normirovannogo polya”, Izv. AN SSSR. Ser. mat., 33:6 (1969), 1296–1323 | MR | Zbl