Geodesic
Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields
Informatics and Automation, Algebra, geometry, and number theory, Tome 292 (2016), pp. 191-208.

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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. 
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D. V. Osipov; A. N. Parshin. Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields. Informatics and Automation, Algebra, geometry, and number theory, Tome 292 (2016), pp. 191-208. http://geodesic.mathdoc.fr/item/TRSPY_2016_292_a11/

[1] Arnal S.A., Parshin A.N., “O neprivodimykh predstavleniyakh diskretnykh grupp Geizenberga”, Mat. zametki, 92:3 (2012), 323–330 | DOI | MR | Zbl

[2] Beloshapka I., Gorchinskiy S., Irreducible representations of finitely generated nilpotent groups, E-print, 2015, arXiv: math/1508.06808 [math.RT] | DOI | MR

[3] Bernstein J., Draft of: Representations of $p$-adic groups, Lectures written by K.E. Rumelhart, Harvard Univ., 1992 http://www.math.tau.ac.il/~bernstei/Unpublished\textunderscore texts/unpublished\textunderscore texts/Bernstein93new-harv.lect.from-chic.pdf

[4] Dixmier J., Les $C^*$-algèbres et leurs représentations, Gauthier-Villars, Paris, 1969 ; Diksme Zh., $C^*$-algebry i ikh predstavleniya, Nauka, M., 1974 | MR | MR

[5] Kahn P., Automorphisms of the discrete Heisenberg group, Preprint, Cornell Univ., Ithaca, 2005 http://www.math.cornell.edu/m/sites/default/files/imported/People/Faculty/Heisen.pdf | MR

[6] Kapranov M., Semiinfinite symmetric powers, E-print, 2001, arXiv: math/0107089 [math.QA]

[7] Osipov D.V., “$n$-Dimensional local fields and adeles on $n$-dimensional schemes”, Surveys in contemporary mathematics, LMS Lect. Note Ser., 347, Ed. by N. Young, Y. Choi, Cambridge Univ. Press, Cambridge, 2008, 131–164 | MR | Zbl

[8] Osipov D.V., “Diskretnaya gruppa Geizenberga i ee gruppa avtomorfizmov”, Mat. zametki, 98:1 (2015), 152–155 | DOI | MR | Zbl

[9] Osipov D.V., Parshin A.N., “Garmonicheskii analiz na lokalnykh polyakh i prostranstvakh adelei. I”, Izv. RAN. Ser. mat., 72:5 (2008), 77–140 | DOI | MR | Zbl

[10] Osipov D.V., Parshin A.N., “Garmonicheskii analiz na lokalnykh polyakh i prostranstvakh adelei. II”, Izv. RAN. Ser. mat., 75:4 (2011), 91–164 | DOI | MR | Zbl

[11] Parshin A.N., “O golomorfnykh predstavleniyakh diskretnykh grupp Geizenberga”, Funkts. analiz i ego pril., 44:2 (2010), 92–96 | DOI | MR | Zbl

[12] Parshin A.N., “Representations of higher adelic groups and arithmetic”, Proc. Int. Congr. Math., Hyderabad (India), Aug. 19–27, 2010, 1, Hindustan Book Agency, New Delhi, 2010, 362–392 | MR

[13] Parshin A.N., “Zapiski o formule Puassona”, Algebra i analiz, 23:5 (2011), 1–54 | MR

[14] Weil A., “Fonction zêta et distributions”, Séminaire Bourbaki 1965/66, Exp. 312, Soc. math. France, Paris, 1995, 523–531 | MR

[15] Weil A., Basic number theory, Grundl. Math. Wiss., 144, 3rd ed., Springer, Berlin, 1974 ; Veil A., Osnovy teorii chisel, Mir, M., 1972 | MR | Zbl | MR