Maximal singular loci of Schubert varieties in SL(n)/B

Transactions of the American Mathematical Society

Volumn 355, Issue 10, 2003, Pages 3915-3945

  Billey, Sara C ^a,b   Warrington, Gregory S ^c,d  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

^c UNIVERSITY OF MASSACHUSETTS   (United States)

^d UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242382109     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03019-8     Document Type: Article

References (31)

1. A. Beilinson and J. Bernstein, Localization of g-modules, C. R. Acad. Sci. Paris Ser. I Math 202 (1981), 15-18. MR 82k:14015
2. S. Billey, Pattern avoidance and rational smoothness of Schubert varieties, Adv. Math. 139 (1998), no. 1, 141-156. MR 99i:14058
3. S. Billey and V. Lakshmibai, Singular Loci of Schubert Varieties, Progress in Mathematics, no. 182, Birkhäuser, 2000. MR 2001j:14065
4. S. Billey and T. K. Lam, Vexillary elements in the hyperoctahedral group, J. Alg. Combin. 8 (1998), no. 2, 139-152. MR 2000d:05124
5. S. Billey and G. Warrington, Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations, J. Alg. Comb. 13 (2001), 111-136.
6. F. Brenti, A combinatorial formula for Kazhdan-Lusztig polynomials, Invent. Math. 118 (1994), no. 2, 371-394. MR 96c:20074
7. _, Combinatorial expansions of Kazhdan-Lusztig polynomials, J. London Math. Soc. 55 (1997), no. 2, 448-472. MR 99a:05143
8. _, Kazhdan-Lusztig polynomials and R-polynomials from combinatorial point of view, Discrete Math 193 (1998), no. 1-3, 93-116. MR 2000c:05154
9. F. Brenti and R. Simion, Explicit formulae for some Kazhdan-Lusztig polynomials, J. Alg. Comb. 11 (2000), no. 3, 187-196. MR 2001e:05137
10. M. Brion and P. Polo, Generic singularities of certain Schubert varieties, Math. Z. 231 (1999), no. 2, 301-324. MR 2000f:14078
11. J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjectures and holonomic systems, Invent. Math. 64 (1981), 387-410. MR 83e:22020
12. J. B. Carrell and J. Kuttler, On the smooth points of T-stable varieties in G/B and the Peterson map, Invent. Math. 151 (2003), no. 2, 353-379.
13. C. Chevalley, Sur les décompositions cellulaires des espaces G/B, Proceedings of Symposia in Pure Mathematics 66 (1994), no. Part I, 1-25. MR 95e:14041
14. A. Cortez, Singularites generiques et quasi-resolutions des variétés de Schubert pour le groupe lineaire, C. R. Acad. Sci. Paris Ser. I Math. 33 (2001), 561-566.
15. V. Deodhar, Local Poincaré duality and non-singularity of Schubert varieties, Comm. Algebra 13 (1985), 1379-1388. MR 861:14015
16. W. Fulton, Young tableaux; with applications to representation theory and geometry, London Mathematical Society Student Texts, vol. 35, Cambridge University Press, New York, 1997. MR 99f:05119
17. V. Gasharov, Sufficiency of Lakshmibai-Sandhya singularity conditions for Schubert varieties, Compositio Math. 126 (2001), no. 1, 47-56. MR 2002d:14078
18. J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge University Press, 1990. MR 92h:20002
19. C. Kassel, A. Lascoux, and C. Reutenauer, The singular locus of a Schubert variety, IRMA Prepublication (2001); to appear in J. Algebra.
20. D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 81j:20066
21. V. Lakshmibai and B. Sandhya, Criterion for smoothness of Schubert varieties in SL(n)/B, Proc. Indian Acad. Sci. (Math Sci.) 100 (1990), no. 1, 45-52. MR 91c:14061
22. V. Lakshmibai and C. S. Seshadri, Singular locus of a Schubert variety, Bull. Amer. Math. Soc. 11 (1984), no. 2, 363-366. MR 85j:14095
23. A. Lascoux, Polynômes de Kazhdan-Lusztig pour les variétés de Schubert vexillaires, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 6, 667-670. MR 96g:05144
24. A. Lascoux and M.-P. Schützenberger, Polynômes de Kazhdan & Lusztig pour les grassmanniennes, Young tableaux and Schur functors in algebra and geometry (Toruń, 1980), Soc. Math. France, Paris, 1981, pp. 249-266. MR 83i:14045
25. A. Lascoux and M.-P. Schützenberger, Schubert polynomials and the Littlewood-Richardson rule, Letters in Math. Physics 10 (1985), 111-124. MR 87g:20021
26. L. Manivel, Generic singularities of Schubert varieties, arXiv:math.AG/0105239 (2001).
27. L. Manivel, Le lieu singulier des variétés de Schubert, Internat. Math. Res. Notices (2001), no. 16, 849-871.
28. P. Polo, Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups, Represent. Theory 3 (1999), 90-104, (electronic). MR 2000j:14079
29. B. Shapiro, M. Shapiro, and A. Vainshtein, Kazhdan-Lusztig polynomials for certain varieties of incomplete flags, Discrete Math. 180 (1998), 345-355. MR 99b:14054
30. J. Stembridge, On the fully commutative elements of Coxeter groups, J. Alg. Combin. 5 (1996), no. 4, 353-385. MR 97g:20046
31. A. V. Zelevinskiǐ, Small resolutions of singularities of Schubert varieties, Functional Anal. Appl. 17 (1983), no. 2, 142-144. MR 85b:14069