Geodesic
On compression of Bruhat–Tits buildings
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Tome 325 (2005), pp. 163-170 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Consider an affine Bruhat–Tits building Latn of type $A_{n-1}$ and the complex distance in $\mathrm{Lat}_n$, i.e., the complete system of invariants of a pair of vertices of the building. An element of the Nazarov semigroup is a lattice in the duplicated $p$-adic space $\mathbb Q_p^n\oplus\mathbb Q_p^n$. We investigate the behavior of the complex distance with respect to the natural action of the Nazarov semigroup on the building. Bibliography: 18 titles. 
@article{ZNSL_2005_325_a9,
     author = {Yu. A. Neretin},
     title = {On compression of {Bruhat{\textendash}Tits} buildings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {163--170},
     year = {2005},
     volume = {325},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a9/}
}
TY  - JOUR
AU  - Yu. A. Neretin
TI  - On compression of Bruhat–Tits buildings
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 163
EP  - 170
VL  - 325
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a9/
LA  - ru
ID  - ZNSL_2005_325_a9
ER  - 
%0 Journal Article
%A Yu. A. Neretin
%T On compression of Bruhat–Tits buildings
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 163-170
%V 325
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a9/
%G ru
%F ZNSL_2005_325_a9
Yu. A. Neretin. On compression of Bruhat–Tits buildings. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XII, Tome 325 (2005), pp. 163-170. http://geodesic.mathdoc.fr/item/ZNSL_2005_325_a9/

[1] K. Brown, Buildings, Springer-Verlag, New York, 1989 | MR

[2] W. Fulton, “Eigenvalues of sums of Hermitian matrices (after A. Klyachko)”, Seminaire Bourbaki, Vol. 1997/98, Exposes 835–849, Asterisque, 252, Societe Mathematique de France, Paris, 1998, 255–269 | MR | Zbl

[3] P. Garrett, Buildings and Classical Groups, Chapmane Hall, London, 1997 | MR | Zbl

[4] Y. Ji, L. Guivarch, J. Taylor, Compactifications of Symmetric Spaces, Birkhauser Boston, Inc., Boston, 1998 | MR

[5] Kh. Koufany, “Contractions of angles in symmetric cones”, Publ. Res. Inst. Math. Sci., 38:2 (2002), 227–243 | DOI | MR | Zbl

[6] V. B. Lidskii, “Neravenstva dlya sobstvennykh i singulyarnykh chisel”, Dobavlenie k vtoromu, tretemu, chetvertomu izdaniyu knigi F. R. Gantmakher, Teoriya matrits, M., 1966, 1976, 1988 | MR

[7] I. G. Macdonald, Spherical functions on a group of $p$-adic type, Publ. Ramanujan Inst., Madras, 1972 ; Uspekhi mat. nauk, 28:5 (1973), 155–224 | MR | MR | Zbl

[8] I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ediction, Clarendon Press, Oxford, 1995 ; I. Makdonald, Simmetricheskie funktsii i mnogochleny Kholla, Mir, M., 1985 | MR | Zbl | MR

[9] M. L. Nazarov, “The oscillator semigroup over nonarchimedian field”, J. Funct. Anal., 128 (1995), 384–438 | DOI | MR | Zbl

[10] V. Yu. Nazarov, Yu. G. Neretin, G. Olshanskii, “Semi-groupes engendrés par la représentation de Weil du groupe symplectique de dimension infinie”, C. R. Acad. Sci. Paris Sér. I Math., 309:7 (1989), 443–446 | MR | Zbl

[11] Yu. A. Neretin, “Ob odnoi polugruppe operatorov v bozonnom prostranstve Foka”, Funkts. anal. i prilozh., 24:2 (1990), 63–73 | MR | Zbl

[12] Yu. Neretin, Categories of symmetries and infinite-dimensional groups, Oxford University Press, New York, 1996 ; Yu. A. Neretin, Kategorii simmetrii i beskonechnomernye gruppy, Editorial URSS, 1998 | MR | Zbl | MR

[13] Yu. A. Neretin, “Hinges and the Study–Semple–Satake–Furstenberg–De Concini–Procesi–Oshima boundary”, Kirillov's Seminar on Representation Theory, Amer. Math. Soc. Transl. Ser. 2, 181, Amer. Math. Soc., Providence, RI, 1998, 165–230 | MR | Zbl

[14] Yu. A. Neretin, “Konformnaya geometriya simmetricheskikh prostranstv i obobschennye drobno-lineinye otobrazheniya Kreina–Shmulyana”, Mat. sb., 190:2 (1999), 93–122 | MR | Zbl

[15] Yu. A. Neretin, “Jordan angles and triangle inequality in Grassmannian manifold”, Geom. Dedicata, 86 (2001), 403–432 | DOI | MR

[16] Yu. A. Neretin, “Beta-funktsiya ansamblya Bryua–Titsa i deformatsiya prostranstva $L^2$ na prostranstve reshetok”, Mat. sb., 194:12 (2003), 31–62 | MR | Zbl

[17] A. Weil, “Sur certains groupes d'operateurs unitaires”, Acta Math., 111 (1964), 143–211 ; Matematika (sbornik perevodov), 13:5 (1969), 33–44 | DOI | MR | Zbl

[18] A. Weil, Basic number theory, Springer-Verlag, New York, 1967 ; A. Veil, Osnovy teorii chisel, Mir, M., 1972 | MR | MR