The nil Hecke ring and singularity of Schubert varieties

Inventiones Mathematicae

Volumn 123, Issue 3, 1996, Pages 471-506

  Kumar, Shrawan ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030556675     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050038     Document Type: Article

References (38)

1. Andersen, H.H.: Schubert varieties and Demazure's character formula. Invent. Math. 79 (1985) 611-618
2. Bernstein, I.N., Gel'fand, I.M., Gel'fand, S.I.: Schubert cells and cohomology of the spaces G/P. Russian Math. Surveys 28 (1973) 1-26
3. Boe, B.D.: Kazhdan-Lusztig polynomials for hermitian symmetric spaces. Trans. A.M.S. 309 (1988) 279-294
4. Bourbaki, N.: Groupes et Algèbres de Lie, Chaps. IV-VI. Hermann, Paris 1968
5. Carrell, J.B.: The Bruhat graph of a Coxeter group, a conjecture of Deodhar, and rational smoothness of Schubert varieties. Proc. Symp. Pure Math. 56 (1994) (edited by W. J. Haboush and B.J. Parshall) 53-61
6. Carrell, J.B.: On the singular locus of a Schubert variety: A survey. (1994) Preprint
7. Carrell, J.B.: The span of the tangent cone of a Schubert variety. (1995) Preprint
8. Cline, E., Parshall, B., Scott, L.: Cohomology, hyperalgebras and representations. J. Algebra 63 (1980) 98-123
9. Deodhar, V.V.: Local Poincaré duality and non-singularity of Schubert varieties. Comm. Algebra 13 (1985) 1379-1388
10. Deodhar, V.V.: A brief survey of Kazhdan-Lusztig theory and related topics, Proc. Symp. Pure Math. 56 (1994) (edited by W.J. Haboush and B.J. Parshall) 105-124
11. Dyer, MJ.: The nil Hecke ring and Deodhar's conjecture on Bruhat intervals. Invent. Math. 111 (1993) 571-574
12. Fulton, W.: Introduction to Intersection Theory in Algebraic Geometry. CBMS regional conference series in Mathematics no. 54 (1984) Am. Math. Soc.
13. Harris, J.: Algebraic Geometry. Springer, Berlin Heidelberg New York 1992
14. Hartshorne, R.: Algebraic Geometry. Springer, Berlin Heidelberg New York 1977
15. Jantzen, J.C.: Moduln mit einem hochsten Gewicht. LNM vol. 750, Springer, Berlin Heidelberg New York 1979
16. Joseph, A.: On the variety of a highest weight module. J. Algebra 88 (1984) 238-278
17. Joseph, A.: On the Demazure character formula. Ann. Sci. Éc. Norm. Sup. 18 (1985) 389-419
18. Kac, V.G.: Infinite Dimensional Lie Algebras. Third edition, Cambridge University Press 1990
19. Kac, V.G., Peterson, D.H.: Regular functions on certain infinite-dimensional groups. In: Arithmetic and Geometry-II, M. Artin, J. Tate (eds.), Birkhäuser (1983) 141-166
20. Kazhdan, D., Lusztig, G.: Representations of Coxeter groups and Hecke algebras. Invent. Math. 53 (1979) 165-184
21. Kostant, B., Kumar, S.: The nil Hecke ring and cohomology of G/P for a Kac-Moody group G. Adv. Math. 62 (1986) 187-237
22. Kostant, B., Kumar, S.: T-equivariant K-theory of generalized flag varieties. J. Differ. Geom. 32 (1990) 549-603
23. Kumar, S.: Demazure character formula in arbitrary Kac Moody setting. Invent. Math. 89 (1987) 395-423
24. Kumar, S.: The nil Hecke ring and singularity of Schubert varieties. In: Lie Theory and Geometry (in honor of Bertram Kostant), J.-L. Brylinski et. al. (eds.), Progress in Math. vol. 123, Birkhäuser (1994) 497-507
25. Lakshmibai, V.: Singular loci of Schubert varieties for classical groups. Bull. A.M.S. 16 (1987) 83-90
26. Lakshmibai, V., Seshadri C.S.: Singular locus of a Schubert variety. Bull. A.M.S. 11 (1984) 363-366
27. Mathieu, O.: Formules de caractères pour les algèbres de Kac-Moody générales. Astérisque no. 159-160 (1988) 1-267
28. Mumford, D.: The Red Book of Varieties and Schemes. LNM vol. 1358, Springer, Berlin Heidelberg New York (1988)
29. Polo, P.: On Zariski tangent spaces of Schubert varieties, and a proof of a conjecture of Deodhar. Indag. Math., n.s., 5 (1994) 483-493
30. Ramanathan, A.: Schubert varieties are arithmetically Cohen-Macaulay. Invent. Math. 80 (1985) 283-294
31. Ramanathan, A.: Equations defining Schubert varieties and Frobenius splitting of diagonals. Publ Math. IHES no. 65 (1987) 61-90
32. Rossmann, W.: Equivariant multiplicities on complex varieties. Astérisque no. 173-174 (1989) 313-330
33. Ryan, K.M.: On Schubert varieties in the flag manifold of SL(n, ℂ). Math. Ann. 276 (1987) 205-224
34. Seshadri, C.S.: Line bundles on Schubert varieties. In: Vector Bundles on Algebraic Varieties, Tata Institute of Fundamental Research, Bombay Colloquium, Oxford University Press (1987) 499-528
35. Slodowy, P.: On the geometry of Schubert varieties attached to Kac-Moody Lie-algebras. Can. Math. Soc. Conf. Proc. on 'Algebraic Geometry' (Vancouver) vol. 6 (1984) 405-442
36. Wolper, J.S.: A combinatorial approach to the singularities of Schubert varieties. Adv. Maths. 76 (1989) 184-193
37. Wolper, J.S.: The Riccati flow and singularities of Schubert varieties. Proceedings of the AMS 123 (1995) 703-709
38. Whitney, H.: Complex Analytic Varieties. Addison-Wesley Publishing Company 1972