A multiplicative property of quantum flag minors

Representation Theory

Volumn 7, Issue 6, 2003, Pages 164-176

  Caldero, Ph ^a  

^a UNIVERSITÉ LYON 1   (France)

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EID: 1842763824     PISSN: 10884165     EISSN: None     Source Type: Journal    
DOI: 10.1090/S1088-4165-03-00156-0     Document Type: Article

References (24)

1. A. Berenstein and A. Zelevinsky, String bases for quantum groups of type Ar, I. M. Gel 0 fand Seminar, 51–89, Adv. Soviet Math., 16, Part 1, Amer. Math. Soc., Providence, RI, (1993). MR 94g:17019
2. A. Berenstein and A. Zelevinski, Tensor product multiplicities, canonical bases and totally positive varieties, Invent. Math., 143 (2001), 77–128. MR 2002c:17005
3. K. Bongartz, On degenerations and extensions of finite-dimensional modules, Adv. Math., 121, (1996), no. 2, 245–287. MR 98e:16012
4. P. Caldero, Adapted algebras for the Berenstein-Zelevinky conjecture, math.RT/0104165.
5. P. Caldero, On the q-commutations in Uq(n) at roots of one, J. Algebra, 210, (1998), no. 2, 557-575. MR 99i:17014
6. C. De Concini and V.G. Kac, Representations of quantum groups at roots of 1, Progress in Math., 92, Birkhäuser Boston (1990), 471-506. MR 92g:17012
7. C. De Concini, C. Procesi, Quantum Schubert cells and representations at roots of 1, Alge- braic groups and Lie groups, 127-160, Austral. Math. Soc. Lect. Ser., 9, Cambridge Univ. Press, Cambridge, 1997. MR 99i:20067
8. S. Fomin, A. Zelevinsky, Cluster algebras I: Foundations, math.RT/0104151.
9. M. Kashiwara, On Crystal Bases, Canad. Math. Soc., Conference Proceed., 16, (1995), 155-195. MR 97a:17016
10. B. Leclerc and A. Zelevinsky, Quasicommuting families of quantum Plcker coordinates, Kirillov’s seminar on representation theory, 85–108, Amer. Math. Soc. Transl. Ser. 2, 181, (1998). MR 99g:14066
11. B. Leclerc, M. Nazarov and J-Y Thibon, Induced representations of affine Hecke algebras and canonical bases of quantum groups, ArXiv:Math.QA/0011074.
12. B. Leclerc, Imaginary vectors in the dual canonical basis of Uq(n), ArXiv:Math.QA/0202148.
13. S.Z. Levendorskii and Y.S. Soibelman, Some applications of quantum Weyl group, J. Geom. Phys., 7, (1990), 241-254. MR 92g:17106
14. P. Littelmann, A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Invent. Math., 116, (1994), 329–346. MR 92f:17023
15. P. Littelmann, A plactic algebra for semisimple Lie algebras, Adv. Math. 124 (1996), no. 2, 312–331. MR 98c:17009
16. G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498. MR 90m:17023
17. G. Lusztig, Introduction to quantum groups, Progress in Mathematics, 110, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 94m:17016
18. P. Papi, Convex orderings in affine root systems, J. Algebra 186, (1996), no. 1, 72–91. MR 97m:17028
19. M. Reineke, On the coloured graph structure of Lusztig’s canonical basis, Math. Ann., 307, (1997), 705–723. MR 98i:17018
20. M. Reineke, Multiplicative properties of dual canonical bases of quantum groups, J. Alg., 211, (1999), 134-149. MR 99k:17034
21. C.M. Ringel, Hall algebras and quantum groups, Invent. Math., 101, (1990), 583-592. MR 91i:16024
22. C.M. Ringel, PBW-bases of quantum groups, Journal Reine Angew. Math., 470, (1996), 51-88. MR 97d:17009
23. Y. Saito PBW basis of quantized universal enveloping algebras, Publ. Res. Inst. Math. Sci., 30, (1994), 209–232. MR 95e:17021
24. T. Tanisaki, Killing forms, Harish-Chandra isomorphisms, and universal R -matrices for quantum algebras, in: Infinite analysis, Part A, B (Kyoto, 1991), Adv. Ser. Math. Phys., 16, 941–961, 1992. MR 93k:17040