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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 5, Pages 163–196 (Mi izv308)  

This article is cited in 8 scientific papers (total in 9 papers)

On Bohr–Sommerfeld bases

A. N. Tyurin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr–Sommerfeld (BS) basis. We use the method of Borthwick–Paul–Uribe [3], in which every vector of a BS basis is determined by some half-weight Legendrian distribution coming from a Bohr–Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The advantage of BS bases (compared to the bases of theta functions in [23]) is that we can use the powerful methods of asymptotic analysis of quantum states. This shows that Bohr–Sommerfeld bases are quasiclassically unitary. Thus we can apply these bases to compare the Hitchin connection [11] and the KZ connection defined by the monodromy of the Knizhnik–Zamolodchikov equation in the combinatorial theory (see, for example, [14] and [15]).

DOI: https://doi.org/10.4213/im308

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English version:
Izvestiya: Mathematics, 2000, 64:5, 1033–1064

Bibliographic databases:

MSC: 53C15, 53C55
Received: 28.09.1999

Citation: A. N. Tyurin, “On Bohr–Sommerfeld bases”, Izv. RAN. Ser. Mat., 64:5 (2000), 163–196; Izv. Math., 64:5 (2000), 1033–1064

Citation in format AMSBIB
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\paper On Bohr--Sommerfeld bases
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\vol 64
\issue 5
\pages 163--196
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\issue 5
\pages 1033--1064
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Tyurin, “Non-abelian analogues of Abel's theorem”, Izv. Math., 65:1 (2001), 123–180  mathnet  crossref  crossref  mathscinet  zmath
    2. A. N. Tyurin, “Lattice gauge theories and the Florentino conjecture”, Izv. Math., 66:2 (2002), 425–442  mathnet  crossref  crossref  mathscinet  zmath
    3. Florentino C.A., Mourão J.M., Nunes J.P., “Coherent state transforms and abelian varieties”, J. Funct. Anal., 192:2 (2002), 410–424  crossref  mathscinet  zmath  isi  elib  scopus
    4. F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Florentino C.A., Mourão J.M., Nunes J.P., “Coherent state transforms and vector bundles on elliptic curves”, J. Funct. Anal., 204:2 (2003), 355–398  crossref  mathscinet  zmath  isi  scopus
    6. Proc. Steklov Inst. Math., 246 (2004), 283–302  mathnet  mathscinet  zmath
    7. Smith I., “Symplectic four-manifolds and conformal blocks”, J. London Math. Soc. (2), 71:2 (2005), 503–515  crossref  mathscinet  zmath  isi  elib  scopus
    8. Kontsevich M., Soibelman Y., “Affine structures and non-archimedean analytic spaces”, Unity of Mathematics - IN HONOR OF THE NINETIETH BIRTHDAY OF I.M. GELFAND, Progress in Mathematics, 244, 2006, 321–385  crossref  mathscinet  zmath  isi  scopus
    9. Burns D., Guillemin V., Uribe A., “The spectral density function of a toric variety”, Pure Appl. Math. Q., 6:2 (2010), 361–382  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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