Littelmann paths and brownian paths

Duke Mathematical Journal

Volumn 130, Issue 1, 2005, Pages 127-167

  Biane, Philippe ^a   Bougerol, Philippe ^b   O'Connell, Neil ^c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 28444455259     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-05-13014-9     Document Type: Article

References (28)

1. Y. BARYSHNIKOV, GUEs and queues, Probab. Theory Related Fields 119 (2001), 256-274. MR 1818248
2. A. BERENSTEIN and A. ZELEVINSKY, Total positivity in Schubert varieties, Comment. Math. Helv. 72 (1997), 128-166. MR 1456321
3. _, Tensor product multiplicities, canonical bases and totally positive varieties, Invent. Math. 143 (2001), 77-128. MR 1802793
4. P. BIANE, Équation de Choquet-Deny sur le dual d'un groupe compact, Probab. Theory Related Fields 94 (1992), 39-51. MR 1189084
5. _, "Minuscule weights and random walks on lattices" in Quantum Probability and Related Topics, QP-PQ 7, World Sci., River Edge, N.J. 1992, 51-65. MR 1186654
6. _, Quelques propriétés du mouvement brownien dans un cône, Stochastic Process. Appl. 53 (1994), 233-240. MR 1302912
7. P. BOUGEROL and T. JEULIN, Paths in Weyl chambers and random matrices, Probab. Theory Related Fields 124 (2002), 517-543. MR 1942321
8. N. BOURBAKI, Éléments de Mathématique, fasc. 34: Groupes et algèbres de Lie, Chapitres 4-6, Actualités Sci. Indust. 1337, Hermann, Paris, 1968. MR 0240238
9. _, Éléments de Mathématique, fasc. 38: Groupes et algèbres de Lie, Chapitres 7-8, Actualités Sci. Indust. 1364, Hermann, Paris, 1975. MR 0453824
10. J. J. DUISTERMAAT and G. J. HECKMAN, On the variation in the cohomology of the symplectic form of the reduced phase space, Invent. Math. 69 (1982), 259-268. MR 0674406
11. P. EYMARD and B. ROYNETTE, "Marches aléatoires sur le dual de SU(2)" in Analyse harmonique sur les groupes de Lie (Nancy-Strasbourg, 1973-75), Lecture Notes in Math. 497, Springer, Berlin, 1975, 108-152. MR 0423457
12. S. FOMIN, "Knuth equivalence, jeu de taquin, and thé Littlewood-Richardson rule," Chapter 7, Appendix 1, in Enumerative Combinatorics, Vol. 2, Cambridge Univ. Press, Cambridge, 1999, 413-439. MR 1676282
13. S. FOMIN and A. ZELEVINSKY, Double Bruhat cells and total positivity, J. Amer. Math. Soc. 12 (1999), 335-380. MR 1652878
14. W. FULTON, Young Tableaux: With Applications to Representation Theory and Geometry, London Math. Soc. Stud. Texts 35, Cambridge Univ. Press, Cambridge, 1997. MR 1464693
15. J. GRAVNER, C. A. TRACY, and H. WIDOM, Limit theorems for height fluctuations in a class of discrete space and time growth models, J. Statist. Phys. 102 (2001), 1085-1132. MR 1830441
16. V. GUILLEMIN and S. STERNBERG, Symplectic Techniques in Physics, 2nd ed., Cambridge Univ. Press, Cambridge, 1990. MR 1066693
17. G. J. HECKMAN, Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups, Invent. Math. 67 (1982), 333-356. MR 0665160
18. J. E. HUMPHREYS, Reflection Groups and Coxeter Groups, Cambridge Stud. Adv. Math. 29, Cambridge Univ. Press, Cambridge, 1990. MR 1066460
19. M. KASHIWARA, Crystal bases of modified quantized enveloping algebra, Duke Math. J. 73 (1994), 383-413. MR 1262212
20. F. KNOP, On the set of orbits for a Borel subgroup, Comment. Math. Helv. 70 (1995) 285-309. MR 1324631
21. M. A. A. VAN LEEUWEN, An analogue of jeu de taquin for Littelmann's crystal paths, Sém. Lothar. Combin. 41 (1998), no. B41b. MR 1661263
22. P. LITTELMANN, Paths and root operators in representation theory, Ann. of Math. (2) 142 (1995), 499-525. MR 1356780
23. _, Cones, crystals, and patterns, Transform. Groups 3 (1998), 145-179. MR 1628449
24. _, "The path model, the quantum Frobenius map and standard monomial theory" in Algebraic Groups and Their Representations (Cambridge, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 517, Kluwer, Dordrecht, Germany, 1998, 175-212. MR 1670770
25. N. O'CONNELL, A path-transformation for random walks and the Robinson-Schensted correspondence, Trans. Amer. Math. Soc. 355 (2003), 3669-3697. MR 1990168
26. N. O'CONNELL and M. YOR, Brownian analogues of Burke's theorem, Stochastic Process. Appl. 96 (2001), 285-304. MR 1865759
27. _, A representation for non-colliding random walks, Electron. Comm. Probab. 7 (2002), 1-12. MR 1887169
28. J. W. PITMAN, One-dimensional Brownian motion and the three-dimensional Bessel process, Adv. in Appl. Probab. 7 (1975), 511-526. MR 0375485