Osipov, D. V.; Parshin, A. N. 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. Cited in 3 Documents MSC: 11S23 Integral representations 11S85 Other nonanalytic theory 20H05 Unimodular groups, congruence subgroups (group-theoretic aspects) 20C15 Ordinary representations and characters Keywords:Heisenberg group; representations PDFBibTeX XMLCite \textit{D. V. Osipov} and \textit{A. N. Parshin}, Proc. Steklov Inst. Math. 292, 185--201 (2016; Zbl 1377.11121); translation from Tr. Mat. Inst. Steklova 292, 191--208 (2016) Full Text: DOI arXiv References: [1] S. A. Arnal’ and A. N. Parshin, “On irreducible representations of discrete Heisenberg groups,” Mat. Zametki 92 (3), 323-330 (2012) [Math. Notes 92, 295-301 (2012)]. · Zbl 1264.43007 [2] I. V. Beloshapka and S. O. Gorchinskiy, “Irreducible representations of finitely generated nilpotent groups,” Mat. Sb. 207 (1), 45-72 (2016) [Sb. Math. 207, 41-46 (2016)]; arXiv:math/1508.06808 [math.RT]. · 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] D. V. Osipov, “The discrete Heisenberg group and its automorphism group,” Mat. Zametki 98 (1), 152-155 (2015) [Math. Notes 98, 185-188 (2015)]. · Zbl 1332.22013 [9] D. V. Osipov and A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. I,” Izv. Ross. Akad. Nauk, Ser. Mat. 72 (5), 77-140 (2008) [Izv. Math. 72, 915-976 (2008)]. · Zbl 1222.11137 [10] D. V. Osipov and A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II,” Izv. Ross. Akad. Nauk, Ser. Mat. 75 (4), 91-164 (2011) [Izv. Math. 75, 749-814 (2011)]. · Zbl 1232.11122 [11] A. N. Parshin, “On holomorphic representations of discrete Heisenberg groups,” Funkts. Anal. Prilozh. 44 (2), 92-96 (2010) [Funct. Anal. Appl. 44, 156-159 (2010)]. · Zbl 1232.43005 [12] A. N. Parshin, “Representations of higher adelic groups and arithmetic,” in Proc. Int. Congr. Math., Hyderabad, India, Aug. 19-27, 2010 (Hindustan Book Agency, New Delhi, 2010), Vol. 1, pp. 362-392. · Zbl 1266.11118 [13] A. N. Parshin, “Notes on the Poisson formula,” Algebra Analiz 23 (5), 1-54 (2011) [St. Petersburg Math. J. 23, 781-818 (2012)]. [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.