Bases canoniques et applications
Séminaire Bourbaki : volume 1997/98, exposés 835-849, Astérisque, no. 252 (1998), Exposé no. 847, 20 p. 
@incollection{SB_1997-1998__40__287_0,
     author = {Littelmann, Peter},
     title = {Bases canoniques et applications},
     booktitle = {S\'eminaire Bourbaki : volume 1997/98, expos\'es 835-849},
     series = {Ast\'erisque},
     note = {talk:847},
     pages = {287--306},
     year = {1998},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {252},
     mrnumber = {1685632},
     zbl = {0966.17009},
     language = {fr},
     url = {https://www.numdam.org/item/SB_1997-1998__40__287_0/}
}
TY  - CHAP
AU  - Littelmann, Peter
TI  - Bases canoniques et applications
BT  - Séminaire Bourbaki : volume 1997/98, exposés 835-849
AU  - Collectif
T3  - Astérisque
N1  - talk:847
PY  - 1998
SP  - 287
EP  - 306
IS  - 252
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/SB_1997-1998__40__287_0/
LA  - fr
ID  - SB_1997-1998__40__287_0
ER  - 
%0 Book Section
%A Littelmann, Peter
%T Bases canoniques et applications
%B Séminaire Bourbaki : volume 1997/98, exposés 835-849
%A Collectif
%S Astérisque
%Z talk:847
%D 1998
%P 287-306
%N 252
%I Société mathématique de France
%U https://www.numdam.org/item/SB_1997-1998__40__287_0/
%G fr
%F SB_1997-1998__40__287_0
Littelmann, Peter. Bases canoniques et applications, dans Séminaire Bourbaki : volume 1997/98, exposés 835-849, Astérisque, no. 252 (1998), Exposé no. 847, 20 p.. https://www.numdam.org/item/SB_1997-1998__40__287_0/

[A] T. Ando, Totally positive matrices, Linear Alg. Appl. 90, (1987), 165-219. | Zbl | MR | DOI

[Bo] N. Bourbaki, Groupes et algèbres de Lie, Ch. 2,3, Hermann, Paris, (1972). | MR | Zbl

[BBD] A. Beilinson, J. Bernstein et P.. Deligne, Faisceaux pervers, Astérisque 100, (1982). | Zbl | MR | Numdam

[BFZ] A. Berenstein, S. Fomin et A. Zelevinsky, Parametrizations of canonical bases and totally positive matrices, Adv. Math. 122, (1996), 49-149. | Zbl | MR | DOI

[BZ] A. Berenstein et A. Zelevinsky, Total positivity in Schubert varieties, Comment. Math. Helv. 72, (1997), 128-166. | Zbl | MR | DOI

[CP] V. Chari et A. Pressley, A guide to quantum groups, Cambridge University Press, (1994). | Zbl | MR

[Cr] C. Cryer, The L U-factorization of totally positive matrices, Linear Algebra Appl. 7, (1973), 83-92. | Zbl | MR | DOI

[D] V. V. Deodhar, On some geometric aspects of Bruhat orderings II. The parabolic analogue of Kazhdan-Lusztig polynomials, J. Algebra 111 (1987), 483-506. | Zbl | MR | DOI

[De] P. Desnanot, Complément de la théorie des équations du premier degré, Volland jeune, Paris, (1819).

[F] M. Fekete, Über ein Problem von Laguerre, Briefwechsel zwischen M. Fekete und G. Pólya, Rendiconti del Circ. Mat. Palermo 34 (1912), 89-100, 110-120. | JFM

[FZ] S. Fomin et A. Zelevinsky, Double Bruhat cells and total positivity, Prépublication de l'I.R.M.A. 8, Strasbourg (1998). | Zbl

[FK] I. Frenkel et M. Khovanov, Canonical bases in tensor products and graphical calculus for U q ( 𝔰𝔩 2 ) , Duke Math. J. 87 (1997), 409-480. | Zbl | MR | DOI

[FKK] I. Frenkel, M. Khovanov et A. Kirillov Jr., Kazhdan-Lusztig polynomials and canonical basis, à paraître dans J. Transf. Groups. | Zbl | MR

[GK] F. Gantmacher et M. Krein, Sur les matrices oscillatoires, C. R. Acad. Sci. Paris 201 (1935), 577-579. | Zbl

[GP] M. Gasca, et J. M. Peña, On the characterization of totally positive matrices, Approximation theory, spline functions and applications, Kluwer, (1992), 357- 364. | Zbl | MR | DOI

[Ce] M. Geck, Representations of Hecke Algebras at Roots of Unity, Sém. Bourbaki, exp. n° 836, novembre 1997, à paraître dans Astérisque. | Numdam | Zbl | MR | EuDML

[J] M. A. Jimbo, A q -analogue of U ( 𝔤𝔩 ( N + 1 ) ) , Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247-252. | Zbl | MR | DOI

[Ka1] M. Kashiwara, On the crystal bases of the q -analogue of universal enveloping algebras, Duke Math. J. 63 (1991), 465-516. | Zbl | MR | DOI

[Ka2] M. Kashiwara, Crystal bases of modified quantized enveloping algebras, Duke Math. J. 73 (1994), 383-413. | Zbl | MR | DOI

[KL] D. Kazhdan et G. Lusztig, Representation of Coxeter groups and Hecke algebras, Inv. Math. 53 (1979), 165-184. | Zbl | MR | EuDML | DOI

[Ko] B. Kostant, The solution to a generalized Toda lattice and representation theory, Adv. in Math. 34 (1979), 195-338. | Zbl | MR | DOI

[LS] A. Lascoux et M.-P. Schützenberger, Polynômes de Kazhdan-Lusztig pour les grassmanniennes, Astérisque 87-88 (1981), 249-266. | Zbl | MR | Numdam

[Lo] C. Loewner, On totally positive matrices, Math. Z. 63 (1955), 338-340. | Zbl | MR | EuDML | DOI

[Lu1] G. Lusztig, Introduction to quantum groups, Progress in Math. 110, Birkhäuser, Boston, 1993. | Zbl | MR

[Lu2] G. Lusztig, Total positivity in reductive groups, Lie Theory and Geometry: in honor of Bertran Kostant, Progress in Math. 123, Birkhäuser, Boston (1994), 531-568. | Zbl | MR

[Lu3] G. Lusztig, Total positivity and canonical bases, Algebraic groups and Lie Groups, Austr. Math. Soc. Lect. Series 9, Cambridge Univ. Press (1997), 281-295. | Zbl | MR

[Lu4] G. Lusztig, Total positivity in partial flag manifolds, Representation Theory 2 (1998), 70-78. | Zbl | MR | DOI

[Lu5] G. Lusztig, Canonical bases arising from quantized enveloping algebras II, Common trends in mathematics and quantum field theories, Progr. Theor. Phys. Suppl. 102 (1990), 175-201. | Zbl | MR | DOI

[Lu6] G. Lusztig, Canonical bases arising from quantized enveloping algebras, JAMS. 3 (1990), 447-498. | Zbl | MR

[Lu7] G. Lusztig, Quivers, perverse sheaves and quantum enveloping algebras, JAMS 4 (1991), 365-421. | Zbl | MR

[Lu8] G. Lusztig, Introduction to total positivity, prépublication (1998). | MR | Zbl | DOI

[Ma] O. Mathieu, Bases des représentations des groupes simples complexes, Sém. Bourbaki, exp. n° 743, Astérisque 201-203 (1991), 421-442. | Numdam | Zbl | MR | EuDML

[Mu] T. Muir, The theory of determinants in the historical order of development, 2nd edition, vol. 1, Macmillan, London (1906). | JFM

[R1] K. Rietsch, The infinitesimal cone of a totally positive semigroup, Proc. AMS 125 (1997), 2565-2570. | Zbl | MR | DOI

[R2] K. Rietsch, An algebraic cell decomposition of the nonnegative part of a flag variety, à paraître dans J. Algebra. | Zbl | MR

[R3] K. Rietsch, Intersections of Bruhat cells in real flag varieties, Internat. Math. Res. Notices 13 (1997), 623-640. | Zbl | MR | DOI

[Sc] I. Schoenberg, Über variationsvermindernde lineare Transformationen, Math. Z. 32 (1930), 321-322. | JFM | MR | EuDML | DOI

[W] A. M. Whitney, A reduction theorem for totally positive matrices, J. d'Analyse Math. 2 (1952), 88-92. | Zbl | MR | DOI

[Z] A. Zelevinsky, Small resolutions of Schubert varieties, Funk. Anal. App. 17 (1983), 75-77. | Zbl | MR