Dualité de Langlands quantique

Vadim Schechtman

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 1, page 129-158
  • ISSN: 0240-2963

Abstract

top
A review of conjectures due to Drinfeld, Beilinson, Gaitsgory et al. and of results of Gaitsgory on the quantum Langlands correspondence.

How to cite

top

Schechtman, Vadim. "Dualité de Langlands quantique." Annales de la faculté des sciences de Toulouse Mathématiques 23.1 (2014): 129-158. <http://eudml.org/doc/275341>.

@article{Schechtman2014,
abstract = {Un survol des conjectures de Drinfeld, Beilinson, Gaitsgory et al. et de résultats de Gaitsgory sur la correspondance de Langlands quantique.},
author = {Schechtman, Vadim},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {quantum Langlands correspondence; quantum Satake correspondence},
language = {fre},
number = {1},
pages = {129-158},
publisher = {Université Paul Sabatier, Toulouse},
title = {Dualité de Langlands quantique},
url = {http://eudml.org/doc/275341},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Schechtman, Vadim
TI - Dualité de Langlands quantique
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 1
SP - 129
EP - 158
AB - Un survol des conjectures de Drinfeld, Beilinson, Gaitsgory et al. et de résultats de Gaitsgory sur la correspondance de Langlands quantique.
LA - fre
KW - quantum Langlands correspondence; quantum Satake correspondence
UR - http://eudml.org/doc/275341
ER -

References

top
  1. Arinkin (D.), Gaitsgory (D.).— Singular support of coherent sheaves, and the geometric Langlands conjecture, arXiv :1201.6343. Zbl06395112
  2. Beilinson (A.), Bernstein (J.).— A proof of Jantzen conjectures, I.M.Gelfand Seminar, Adv. Soviet Math. (AMS), 16, Part 1, p. 1-51 (1993). Zbl0790.22007MR1237825
  3. Beilinson (A.), Drinfeld (V.).— Quantization of Hitchin integrable system and Hecke eigensheaves. 
  4. Beilinson (A.), Schechtman (V.).— Determinant bundles and Virasoro algebras, Comm. Math. Phys., 118, p. 651-701 (1988). Zbl0665.17010MR962493
  5. Belavin (A.), Polyakov (A.), Zamolodchikov (A.).— Infinite conformal symmetry in 2D quantum field theory, Nucl. Phys. B241, p. 333-380 (1984). Zbl0661.17013
  6. Berezin (F.A.), Gelfand (I.M.).— Quelques remarques sur la théorie des fonctions sphériques sur les variétés symétriques riemanniennes (russe), Trudy MMO (Travaux de la Société Mathématique de Moscou) 5, p. 311-351 (1956). Zbl0075.11803MR86266
  7. Braverman (A.), Gaitsgory (D.).— Geometric Eisenstein series, Invent. Math. 150, p. 287-384 (2002). Zbl1046.11048MR1933587
  8. Bezrukavnikov (R.), Finkelberg (M.), Schechtman (V.).— Factorizable sheaves and quantum groups, Lect. Notes in Math. 1691, Springer-Verlag, Berlin (1998). Zbl0938.17016MR1641131
  9. Finkelberg (M.), Mirkovich (I.).— Semiinfinite flags. I. Case of global curve 1  ; Feigin (B.), Finkelberg (M.), Kuznetsov (A.), Mirkovich (I.), Semiinfinite flags. II. Local and global intersection cohomology of quasimaps spaces, dans : Differential topology, infinite-dimensional Lie algebras, and applications, p. 81-112 et p. 113-148, AMS Transl. Ser. 2, 194, Providence, RI (1999). Zbl1076.14511MR1729360
  10. Frenkel (E.), Ben-Zvi (D.).— Vertex algebras and algebraic curves, 2nd Edition, Math. Surveys and Monographs 88, AMS, Providence, RI (2004). Zbl1106.17035MR2082709
  11. Frenkel (E.), Gaitsgory (D.), Vilonen (K.).— Whittaker patterns in the geometry of moduli spaces of bundles on curves, Ann. Math. 153, p. 699-748 (2001). Zbl1070.11050MR1836286
  12. Frenkel (E.), Gaitsgory (D.), Vilonen (K.).— On the geometric Langlands conjecture, JAMS 15, p. 367-417 (2001). Zbl1071.11039MR1887638
  13. Gaitsgory (D.).— Twisted Whittaker models and factorizable sheaves, Selecta Math. (N.S.) 13, p. 617-659 (2008). Zbl1160.17009MR2403306
  14. Gaitsgory (D.).— On a vanishing conjecture appearing in the Geometric Langlands correspondence, Ann. Math. 160, p. 617-682 (2004). Zbl1129.11050MR2123934
  15. Ginzburg (V.).— Perverse sheaves on a loop group and Langlands duality, arXiv :alg-geom/2511007. MR1092806
  16. Helgason (S.).— Groups and geometric analysis, Academic Press (1984). Zbl0543.58001MR754767
  17. Kazhdan (D.), Lusztig (G.).— Tensor structures arising from affine Lie algebras I-IV JAMS, 6, p. 905-947, p. 949-1011 (1993) ; 7, p. 335-381, p. 383-453 (1994). Zbl0786.17017MR1186962
  18. Lafforgue (L.).— Chtoukas de Drinfeld et correspondance de Langlands, Inv. Math. 147, p. 1-241 (2002). Zbl1038.11075MR1875184
  19. Laumon (G.).— Transformation de Fourier généralisée, arXiv :alg-geom/9603004. 
  20. Maaß(H.).— Über eine neue Art von nichtanalytichen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 21, p. 141-183 (1949). Zbl0033.11702MR31519
  21. Macdonald (I.G.).— Spherical functions on a 𝔭 -adic Chevalley group, Bull. Amer. Math. Soc. Vol. 74, 3, p. 520-525 (1968). Zbl0273.22012MR222089
  22. Mirković (I.), Vilonen (K.).— Geometric Langlands duality and representations of algebraic groups over commutative rings, Ann. of Math. (2) 166, p. 95-143 (2007). Zbl1138.22013MR2342692
  23. Satake (I.).— Theory of spherical functions on reductive algebraic groups over 𝔭 -adic fields, Publ. Math. IHES 18, p. 5-69 (1963). Zbl0122.28501MR195863
  24. Stoyanovsky (A.).— On quantization of the geometric Langlands correspondence, arXiv :math/9911108. Zbl1311.81213
  25. Stoyanovsky (A.).— Quantum Langlands duality and Conformal field theory, arXiv :math/0610974. Zbl1174.81005

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.