Books

), Proceedings of the NATO Advanced Study Institute on`Representation theories and Algebraic Geometry", Montreal, 1997, NATO ASI series, Series C: Mathematical and Physical sciences, vol. 514, Kluwer Academic Publishers.

tex file

Degeneracy schemes, Quiver schemes and Schubert varieties

(with

P. Magyar

), IMRN, no:12, 1998, p.627-640.

Frobenius splittings and blow-ups

(with V. B. Mehta and A. J. Parameswaran), J.Alg., vol 208 (1998), 101-128.

Schubert varieties, toric varieties and ladder determinantal varieties

(with N. Gonciulea), Ann. Inst. Fourier, t.47, 1997, 1013-1064.

Degenerations of flag and Schubert varieties to toric varieties

(with N. Gonciulea),

Transformation Groups

Bases for Quantum Demazure modules

Representations of Groups , Banff 1994, CMS Conference Proceedings, vol 16, Canadian Math. Society (1995).

Multiplicities of singular points on a Schubert variety

C.R. Acad. Sci., Paris, t.321,Serie 1, (1995), 215-218.

Tangent spaces to Schubert varieties

Math. Research. Letters, 2 (1995), 473-477

Criterion for smoothness of Schubert varieties in Sp(2n)/B

(with M. Song), Journal of Algebra, 189 (1997), 332-352 .

Gröbner bases and standard monomial bases

(with N. Gonciulea)

C. R. Acad. Sci.Paris Sér. I Math. 322, 1996, no. 3, 255-260.

List of Publications

1. Cohomology of line bundles on G/B (with C.Musili and C.S.Seshadri)

Ann. Sci. E.N.S. (1974), 89-138

2. Kempf varieties

J. Ind. Math. Soc., Vol. 40 (1976), 299-349.

3. Geometry of G/P - II (with C.S.Seshadri)

Proc. Ind. Acad. Sci., 87A (1978), 1-54

4. Geometry of G/P - III (with C.Musili and C.S.Seshadri)

Proc. Ind. Acad. Sci., 87A (1978), 93-77

5. Geometry of G/P - IV (with C.Musili and C.S.Seshadri)

Proc. Ind. Acad. Sci., 88A (1979), 279-362

6. Geometry of G/P (with C.Musili and C.S. Seshadri)

Bull. A.M.S., (1979), 432-435

7.Arithmetic Cohen-Macauleyness and Arithmetic Normality for Schubert varieties (with C. DeConcini)

Amer. J. Math., Vol. 103 (1981), 835-850

8. On the normality of rings of Schubert varieties (with C. Huneke)

Proc. Ind. Acad. Sci., Vol. 91 (1982), 65-71

9. Singular locus of a Schubert variety (with C.S. Seshadri)

Bull. A.M.S., Vol. 11 (1984), 363-366

10. A characterization of Kempf varieties and the geometric consequences (with C. Huneke)

J. Alg., Vol. 94 (1985), 52-105

11. Geometry of G/P - V (with C.S. Seshadri)

J. Alg., Vol. 100 (1986), 463-557

12. Bases pour les Representations Fondamentales des Groupes Classiques

Comptes Rendus, 302, Serie I (1986), 387-390

13. Bases pour les Representations Fondamentales des Groupes Classiques II

Comptes Rendus, 302, Serie I (1986), 419-422

14. Bases pour les Representations Fondamentales des Groupes Exceptional $E$ ₆ and $F$ ₇(with K.N.Rajeswari)

Comptes Rendus, 302, Serie I (1986), 575-577

15. Standard monomial theory for $G$ ₂

J. Alg., Vol. 98 (1986), 281-318

16. Geometry of G/P - VI

J. Alg., Vol. 108 (1987), 355-402

17. Geometry of G/P - VII

J. Alg., Vol. 108 (1987), 403-434

18. Geometry of G/P - VIII

J. Alg., Vol. 108 (1987), 435-471

19. Singular loci of Schubert varieties

Bull. A.M.S., Vol. 16 (1987), 83-90

20. Standard monomial theory for $SL$ ₂ (with C.S. Seshadri)

Comptes Rendus, t.305, Serie I (1987), 183-185

21. Multiplicites sur une variete de Schubert dans un minuscule G/P (with J. Weyman)

Comptes Rendus, t.307, Serie I (1988), 993-996

22. Towards a standard monomial theory for exceptional groups (with K.N.Rajeswari)

Contemporary Math., A.M.S., Vol. 88 , 1989

23. Standard monomial theory for $SL$ ₂, (with C.S.Seshadri)

Advanced Studies in Mathematical Physics, Vol. 7 (1989), ``Infinite Dimensional Lie Algebras and Groups", Luminy, p.178-234, Proceedings of the conference held at CIRM, Luminy, Marseille, July 4-8, 1988

24. Criterion for smoothness of Schubert varieties in $SL$ _n (with Sandhya)

Proc. Ind. Acad. Sci. 1990, 45-52 .

25. Standard Monomial Theory for $SL$ _n(with C.S.Seshadri)

Volume dedicated to Dixmier's 65 birthday (published by Birkhauser), Progress in Mathematics 92 (1990).

26. Geometry of G/P - IX, J. Alg, Vol. 130 (1990), 122-165 (with K.N.Rajeswari).
27. Multiplicities of points on a Schubert variety in a minuscule G/P (with J.Weyman, Advances in Math, Vol. 84 (1990), 179-208
28. Schubert varieties and Standard monomial theory , Banach Center Publications, Vol.26, Part 2, PWN-Polish Scientific Publishers, 1990, 315-378, Banach Institute's Proceedings on``Algebraic Groups-their Combinatorics and Representations", 1988.
29. Quantum deformations of Flag Schemes and Schubert schemes , Comptes Rendus, t.313, Serie I, 1991, 121-126 (with Reshetikhin).
30. Quantum deformations of SL(n)/B and its Schubert varieties, ``Special Functions", ICM-90, Satellite Conference Proceedings, Springer-Verlag, 149-168 (with Reshetikhin).
31. Standard Monomial Theory for $ \hat {Sp}(2n)$, ``Special functions", ICM-90 Satellite Conference Proceedings, Springer-Verlag, 127-148.
32. Standard monomial theory and Schubert varieties-a survey, Proceedings of the Conference on ``Algebraic Groups and Applications", 1991, 279-322, Manoj Prakashan (with Seshadri).
33. Degeneracy of Schubert varieties (with C.Huneke), Contemporary \noindent Math., Vol 139, 1992, 181-235.
34. Quantum deformations of Flag and Schubert schemes, (with \noindent N. Reshetikhin), Contemporary Math.,Vol 134, 1992, 145-179.
35. Bases for quantum Demazure modules-I, Geometry and Analysis, Oxford University Press, 1995, 197-219 ( volume dedicated to Profs. M.S.Narasimhan and C.S.Seshadri on their 60th birthdays).
36. Bases for Demazure modules for symmetrizable Kac-Moody algebras , Contemporary.Math., Vol 153, 1993, 59-78 (volume dedicated to Professor R. Steinberg on his 70th birthday).
37. Bases for quantum Demazure modules-II, Proc. Symp. Pure. Math.,vol 56, Part 2, 149-168.
38. Bases for quantum Demazure modules, CMS Conference Proceedings, vol 16, 199-216, Proceedings of the coference on `` Representations of Groups: Lie, Algebraic, Finite,and Quantum", Banff, Alberta, June 1994
39. Tangent spaces to Schubert Varieties, Math. Research Letters 2 (1995), 473-477.
40. Multiplicities of points on a Schubert variety, Comptes Rendus, t.321, Serie I, 1995, 215-218.
41. Frobenius splittings and blow ups (with V.B. Mehta and A.J. Parameswaran), J.Alg., vol 208 (1998), 101-128..
42. Grobner bases and Standard monomial bases (with N. Gonciulea), Comptes Rendus, 322 (1996) 255-360.
43. Degenerations of Flag varieties to Toric varieties, Comptes Rendus, t.321 (1995), 1229-1234.
44. Degenerations of Flag and Schubert varieties to Toric varieties, Transformation Groups, vol 1, no:3 (1996), 215-248.
45. Criterion for smoothness of Schubert varieties in $Sp_{2n} /B $ (with M. Song), Journal of Algebra, 189 (1997), 332-352 .
>46. Schubert varieties, Toric varieties, and Ladder determinantal varieties (with N. Gonciulea), Ann. Inst. Fourier, t.47, 1997, 1013-1064.
47. Standard monomial Theory for Bott-Samelson

varieties

(

), Comptes Rendus, t.324, 1997, 1211-1215.

48. Standard monomial Theory for Bott-Samelson varieties (with P. Magyar), Comptes Rendus.,t.324., Serie I, 1997, 1211-1215.
49. Degeneracy Schemes, Quiver Schemes, and Schubert varieties (with P. Magyar), IMRN, no:12, 1998, p.627-640.
50. Standard monomial Theory for Bott-Samelson

varieties of $GL(n)$}(with P. Magyar)

, Publications RIMS, vol 34, \# 3, 1998,

229-248.

51. Standard Monomial Theory and Applications (with P.

Littelmann and P. Magyar), Proceedings of the NATO Advanced Study Institute on``Representation theories and Algebraic Geometry", Montreal, 1997, NATO ASI series,Series C: Mathematical and Physical sciences, vol. 514, Kluwer Academic Publishers.

52. Singular loci of Schubert varieties and Ladder determinantal varieties (with N. Gonciulea), J. Alg., 232 (2000),

360-395.

53. On the tangent space to a Schubert variety - I , J.Alg.,230 (2000), 222-244.
54. On the tangent space to a Schubert variety-II , J.Alg., 224 (2000), 167-197.
55. Singular loci of varieties of complexes, J. PureAnd Applied Algebra, 152 (2000), 217-230.
56. On the singular locus of a Schubert variety, (with

S. Billey), J. Ramanujan Math. Soc., 15, no:3 (2000), 155-223.

57. Standard monomial Theory for Bott-Samelson varieties

of semisimple algebraic groups

(with P. Littelmann and P.Magyar), to appear in Composito Math.

58. Multiplicities at Singular Points of Schubert Varieties in the Grassmannian, to Appear in Abyanakar's 70th Birthday Proceedings, 2001 (with V. Kreiman).
59. Some affine varieties related to Schubert varieties, to appear in theProceedings of the Irvine meeting on "Invariant Theory".
60. A geometric approach to standard monomial theory (with M. Brion), preprint 2001,
61. Equivariant K-theory and Richardson varieties (with P. Littelmann), preprint 2001,
62. Richardson varieties in the Grassmannian (with V. Kreiman), preprint 2002.

Papers in preparation:

1. Ring of invariants for the SL(n),SO(n) actions ( inpreparation with P. Shukla)
2. Multiplicities of points on Schubert Varieties.
3. The variety XY=0,YX=0,X,Y being square matricesof size n.
60. A criterion for smoothness of Schubert varieties, preprint 2000.
4. L-S path-theory for for Bott-Samelson varieties

Books:

1. Invariant Theory, Comtemporary Mathematics,; A.M.S., Vol. 88 (1987), co-edited with R. Fossum, et al.
2. Singular loci of Schubert varieties,Progress in Math., 182, Birkhauser; (2000), (with S. Billey).
3. The Flag variety, Hermann-Actualites Mathematiques(2001), (with N. Gonciulea).
4. Schubert varieties, (with P. Littelmann, and C.S.Seshadri), in preparation, to be published by Birkhauser.