On an infinite-dimensional limit of the Steinberg representations
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 126-132 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a construction of the Steinberg representation that allows for automatically passing to an infinite-dimensional limit.
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Yu. A. Neretin. On an infinite-dimensional limit of the Steinberg representations. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 126-132. http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a9/

[1] C. W. Curtis, N. Iwahori, R. Kilmoyer, “Hecke algebras and characters of parabolic type of finite groups with $(B,N)$-pairs”, Publ. Math. Inst. Hautes Études Sci., 40 (1971), 81–116 | DOI | MR | Zbl

[2] W. Fulton, Young Tableaux: with Applications to Representation Theory and Geometry, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[3] V. Gorin, S. Kerov, A. Vershik, Finite traces and representations of the group of infinite matrices over a finite field, arXiv: 1209.4945 | MR

[4] J. E. Humphreys, “The Steinberg representation”, Bull. Amer. Math. Soc. (N.S.), 16:2 (1987), 237–263 | DOI | MR

[5] Yu. A. Neretin, Lectures on Gaussian Integral Operators and Classical Groups, EMS, Zürich, 2011 | MR | Zbl

[6] Yu. A. Neretin, “The space $L^2$ on semi-infinite Grassmannian over finite field”, Adv. Math., 250 (2014), 320–350 | DOI | MR | Zbl

[7] Yu. A. Neretin, On multiplication of double cosets for $\mathrm{GL}(\infty)$ over a finite field, arXiv: 1310.1596

[8] R. Steinberg, Collected Papers, Amer. Math. Soc., Providence, Rhode Island, 1997, 580–586 | MR

[9] A. M. Vershik, S. V. Kerov, “On an infinite-dimensional group over a finite field”, Funct. Anal. Appl., 32:3 (1998), 147–152 | DOI | MR | Zbl

[10] A. M. Vershik, S. V. Kerov, “Four drafts on the representation theory of the group of infinite matrices over a finite field”, J. Math. Sci. (N.Y.), 147:6 (2007), 7129–7144 | DOI | MR