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Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields. (English. Russian original) Zbl 1377.11121

Proc. Steklov Inst. Math. 292, 185-201 (2016); translation from Tr. Mat. Inst. Steklova 292, 191-208 (2016).
Summary: We study a natural action of the Heisenberg group of integer unipotent matrices of the third order on the distribution space of a two-dimensional local field for a flag on a two-dimensional scheme.

MSC:

11S23 Integral representations
11S85 Other nonanalytic theory
20H05 Unimodular groups, congruence subgroups (group-theoretic aspects)
20C15 Ordinary representations and characters
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[1] Arnal’, S. A.; Parshin, A. N., On irreducible representations of discrete Heisenberg groups, Mat. Zametki, 92, 323-330, (2012) · Zbl 1264.43007
[2] Beloshapka, I. V.; Gorchinskiy, S. O., Irreducible representations of finitely generated nilpotent groups, Mat. Sb., 207, 45-72, (2016) · Zbl 1365.43006
[3] Bernstein, J., Draft of: representations of p-adic groups, (1992)
[4] J. Dixmier, Les C -algèbres et leurs représentations (Gauthier-Villars, Paris, 1969). · Zbl 0174.18601
[5] Kahn, P., Automorphisms of the discrete Heisenberg group, (2005), Ithaca
[6] M. Kapranov, “Semiinfinite symmetric powers,” arXiv: math/0107089 [math.QA]. · Zbl 1266.11118
[7] Osipov, D. V.; Young, N. (ed.); Choi, Y. (ed.), N-dimensional local fields and adeles on n-dimensional schemes, (2008), Cambridge · Zbl 1144.11078
[8] Osipov, D. V., The discrete Heisenberg group and its automorphism group, Mat. Zametki, 98, 152-155, (2015) · Zbl 1332.22013
[9] Osipov, D. V.; Parshin, A. N., Harmonic analysis on local fields and adelic spaces. I, Izv. Ross. Akad. Nauk, Ser. Mat., 72, 77-140, (2008) · Zbl 1222.11137
[10] Osipov, D. V.; Parshin, A. N., Harmonic analysis on local fields and adelic spaces. II, Izv. Ross. Akad. Nauk, Ser. Mat., 75, 91-164, (2011) · Zbl 1232.11122
[11] Parshin, A. N., On holomorphic representations of discrete Heisenberg groups, Funkts. Anal. Prilozh., 44, 92-96, (2010) · Zbl 1232.43005
[12] Parshin, A. N., Representations of higher adelic groups and arithmetic, in Proc. Int. Congr. Math., Hyderabad, India, Aug. 19-27, 2010, 1, 362-392, (2010) · Zbl 1266.11118
[13] Parshin, A. N., Notes on the Poisson formula, Algebra Analiz, 23, 1-54, (2011)
[14] Weil, A., Fonction zêta et distributions, (1995), Paris
[15] A. Weil, Basic Number Theory, 3rd ed. (Springer, Berlin, 1974), Grundl. Math. Wiss. 144. · Zbl 0326.12001
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