@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}, publisher = {Soci\'et\'e math\'ematique de France}, number = {252}, year = {1998}, mrnumber = {1685632}, zbl = {0966.17009}, language = {fr}, url = {http://archive.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 - http://archive.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 http://archive.numdam.org/item/SB_1997-1998__40__287_0/ %G fr %F SB_1997-1998__40__287_0
Littelmann, Peter. Bases canoniques et applications, in Séminaire Bourbaki : volume 1997/98, exposés 835-849, Astérisque, no. 252 (1998), Talk no. 847, 20 p. http://archive.numdam.org/item/SB_1997-1998__40__287_0/
[A] Totally positive matrices, Linear Alg. Appl. 90, (1987), 165-219. | DOI | MR | Zbl
,[Bo] Groupes et algèbres de Lie, Ch. 2,3, Hermann, Paris, (1972). | MR | Zbl
,[BBD] Faisceaux pervers, Astérisque 100, (1982). | Numdam | MR | Zbl
, et ,[BFZ] Parametrizations of canonical bases and totally positive matrices, Adv. Math. 122, (1996), 49-149. | DOI | MR | Zbl
, et ,[BZ] Total positivity in Schubert varieties, Comment. Math. Helv. 72, (1997), 128-166. | DOI | MR | Zbl
et ,[CP] A guide to quantum groups, Cambridge University Press, (1994). | MR | Zbl
et ,[Cr] The L U-factorization of totally positive matrices, Linear Algebra Appl. 7, (1973), 83-92. | DOI | MR | Zbl
,[D] On some geometric aspects of Bruhat orderings II. The parabolic analogue of Kazhdan-Lusztig polynomials, J. Algebra 111 (1987), 483-506. | DOI | MR | Zbl
,[De] Complément de la théorie des équations du premier degré, Volland jeune, Paris, (1819).
,[F] Problem von Laguerre, Briefwechsel zwischen M. Fekete und G. Pólya, Rendiconti del Circ. Mat. Palermo 34 (1912), 89-100, 110-120. | JFM
, Über ein[FZ] Double Bruhat cells and total positivity, Prépublication de l'I.R.M.A. 8, Strasbourg (1998). | Zbl
et ,[FK] Canonical bases in tensor products and graphical calculus for , Duke Math. J. 87 (1997), 409-480. | DOI | MR | Zbl
et ,[FKK] Kazhdan-Lusztig polynomials and canonical basis, à paraître dans J. Transf. Groups. | MR | Zbl
, et ,[GK] Sur les matrices oscillatoires, C. R. Acad. Sci. Paris 201 (1935), 577-579. | Zbl
et ,[GP] On the characterization of totally positive matrices, Approximation theory, spline functions and applications, Kluwer, (1992), 357- 364. | DOI | MR | Zbl
, et ,[Ce] Representations of Hecke Algebras at Roots of Unity, Sém. Bourbaki, exp. n° 836, novembre 1997, à paraître dans Astérisque. | EuDML | Numdam | MR | Zbl
,[J] A -analogue of , Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247-252. | DOI | MR | Zbl
,[Ka1] On the crystal bases of the -analogue of universal enveloping algebras, Duke Math. J. 63 (1991), 465-516. | DOI | MR | Zbl
,[Ka2] Crystal bases of modified quantized enveloping algebras, Duke Math. J. 73 (1994), 383-413. | DOI | MR | Zbl
,[KL] Representation of Coxeter groups and Hecke algebras, Inv. Math. 53 (1979), 165-184. | DOI | EuDML | MR | Zbl
et ,[Ko] The solution to a generalized Toda lattice and representation theory, Adv. in Math. 34 (1979), 195-338. | DOI | MR | Zbl
,[LS] Polynômes de Kazhdan-Lusztig pour les grassmanniennes, Astérisque 87-88 (1981), 249-266. | Numdam | MR | Zbl
et ,[Lo] On totally positive matrices, Math. Z. 63 (1955), 338-340. | DOI | EuDML | MR | Zbl
,[Lu1] Introduction to quantum groups, Progress in Math. 110, Birkhäuser, Boston, 1993. | MR | Zbl
,[Lu2] Total positivity in reductive groups, Lie Theory and Geometry: in honor of Bertran Kostant, Progress in Math. 123, Birkhäuser, Boston (1994), 531-568. | MR | Zbl
,[Lu3] Total positivity and canonical bases, Algebraic groups and Lie Groups, Austr. Math. Soc. Lect. Series 9, Cambridge Univ. Press (1997), 281-295. | MR | Zbl
,[Lu4] Total positivity in partial flag manifolds, Representation Theory 2 (1998), 70-78. | DOI | MR | Zbl
,[Lu5] Canonical bases arising from quantized enveloping algebras II, Common trends in mathematics and quantum field theories, Progr. Theor. Phys. Suppl. 102 (1990), 175-201. | DOI | MR | Zbl
,[Lu6] Canonical bases arising from quantized enveloping algebras, JAMS. 3 (1990), 447-498. | MR | Zbl
,[Lu7] Quivers, perverse sheaves and quantum enveloping algebras, JAMS 4 (1991), 365-421. | MR | Zbl
,[Lu8] Introduction to total positivity, prépublication (1998). | DOI | MR | Zbl
,[Ma] Bases des représentations des groupes simples complexes, Sém. Bourbaki, exp. n° 743, Astérisque 201-203 (1991), 421-442. | EuDML | Numdam | MR | Zbl
,[Mu] The theory of determinants in the historical order of development, 2nd edition, vol. 1, Macmillan, London (1906). | JFM
,[R1] The infinitesimal cone of a totally positive semigroup, Proc. AMS 125 (1997), 2565-2570. | DOI | MR | Zbl
,[R2] An algebraic cell decomposition of the nonnegative part of a flag variety, à paraître dans J. Algebra. | MR | Zbl
,[R3] Intersections of Bruhat cells in real flag varieties, Internat. Math. Res. Notices 13 (1997), 623-640. | DOI | MR | Zbl
,[Sc] Über variationsvermindernde lineare Transformationen, Math. Z. 32 (1930), 321-322. | DOI | EuDML | JFM | MR
,[W] A reduction theorem for totally positive matrices, J. d'Analyse Math. 2 (1952), 88-92. | DOI | MR | Zbl
,[Z] Small resolutions of Schubert varieties, Funk. Anal. App. 17 (1983), 75-77. | MR | Zbl
,