A remark on universal connections
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A G-minimal model for principal G-bundles
Annales de L'Institut Fourier, Grenoble 32, 205-219 (1982). [pdf]
Geometry of Schubert cells and cohomology of Kac-Moody Lie algebras
J. Diff. Geometry 20, 389-431 (1984). [pdf]
Rational homotopy theory of flag varieties associated to Kac-Moody groups
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Cohomology algebra of Schubert varieties associated to Kac-Moody groups
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A generalization of the Conner conjecture and topology of Stein spaces dominated by C^n
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The nil Hecke ring and cohomology of G/P for a Kac-Moody group G (with B. Kostant)
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A homology vanishing theorem for Kac-Moody algebras with coefficients in the category O
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Non-representability of cohomology classes by bi-invariant forms (Gauge and Kac-Moody groups)
Commu. Math. Physics 106, 177-181 (1986). [pdf]
The nil Hecke ring and cohomology of G/P for a Kac-Moody group G (with B. Kostant)
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T-equivariant K-theory of generalized flag varieties (with B. Kostant)
Proc. Natl. Acad. Sci. USA 84, 4351-4354 (1987). [pdf]
Extension of the category O^g and a vanishing theorem for the Ext functor for Kac-Moody algebras
J. Algebra 108, 472-491 (1987). [pdf]
Demazure character formula in arbitrary Kac-Moody setting
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Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture
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Existence of certain components in the tensor product of two integrable highest weight modules for Kac-Moody algebras
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A refinement of the PRV conjecture
Invent. Math. 97, 305-311 (1989). [pdf]
Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras
Math. Annalen 286, 709-729 (1990). [pdf]
A new geometric invariant associated to the space of flat connections (with K. Guruprasad)
Compositio Math. 73, 199-222 (1990). [pdf]
T-equivariant K-theory of generalized flag varieties (with B. Kostant)
J. Diff. Geometry 32, 549-603 (1990). [pdf]
Proof of Wahl's conjecture on surjectivity of the Gaussian map for flag varieties
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A geometric realization of minimal rak k-type of Harish-Chandra modules for complex s.s. groups (with B. Kostant)
In: "Kazhdan-Lusztig theory and related topics" (ed. by V. Deodhar). Contemporary Mathematics vol. 139 published by AMS, 249-264 (1992). [pdf]
Proof of Wahl's conjecture on surjectivity of the Gaussian map for flag varieties
American J. of Math. 114, 1201-1220 (1992). [pdf]
Cohomology of quantum groups at roots of unity (with V. Ginzburg)
Duke Math. J. 69, 179-198 (1993). [pdf]
Finiteness of local fundamental groups for quotients of affine varieties under reductive groups
Comment. Math. Helvetici 68, 209-215 (1993). [pdf]
Equivariant cohomology with generalized coefficients (with M. Vergne)
Ast\'erisque 215, 109-204 (1993). [pdf]
Toward proof of Lusztig's conjecture concerning negative level representations of affine Lie algebras
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Symmetric and exterior powers of homogeneous vector bundles
Math. Annalen 299, 293-298 (1994). [pdf]
Representations of quantum groups at roots of unity
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Infinite Grassmannians and moduli spaces of G-bundles (with M. S. Narasimhan and A. Ramanathan)
Math. Annalen 300, 41-75 (1994). [pdf]
The nil Hecke ring and singularity of Schubert varieties
In: "Lie theory and geometry (in honor of B. Kostant)" (ed. by J.-L. Brylinski et. al.). Progress in Math. vol. 123, Birkhauser, 497-507 (1994). [pdf]
The nil Hecke ring and singularity of Schubert varieties
Inventiones Math. 123, 471-506 (1996). [pdf]
Shapovalov determinant for restricted and quantized restricted enveloping algebras (with G. Letzter)
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Infinite Grassmannians and moduli spaces of G-bundles
In: "Vector Bundles on Curves- New Directions," (ed. by M.S. Narasimhan). Springer Lecture Notes in Math. vol. 1649, 1-49 (1997). [pdf]
Picard group of the moduli spaces of G-bundles (with M.S. Narasimhan)
Math. Annalen 308, 155-173 (1997). [pdf]
Fusion product of positive level representations and Lie algebra homology
In: "Geometry and physics" (ed. by J.E. Andersen et. al.). Lecture Notes in Pure and Applied Mathematics vol. 184, Marcel Dekker, Inc., 253-259 (1997). [pdf]
Positivity of the cup product in cohomology of flag varieties associated to Kac-Moody groups (with M.V. Nori)
Inter. Math. Res. Not. 14, 757-763 (1998). [pdf]
Frobenius splitting of cotangent bundles of flag varieties (with N. Lauritzen and J. Thomsen)
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Homology of certain truncated Lie algebras
In: "Recent Developments in Quantum Affine Algebras and Related Topics," (ed. by K.C. Misra et. al.). Contemporary Mathematics vol. 248, 309--325 (1999), published by AMS. [pdf]
Frobenius splitting in characteristic zero and the quantum Frobenius map (with P. Littelmann)
J. of Pure and applied Algebra 152, 201--216 (2000). [pdf]
Frobenius splitting of Hilbert schemes of points on surfaces (with J.F. Thomsen)
Math. Annalen 319, 797--808 (2001). [pdf]
Algebraization of Frobenius splitting via quantum groups (with P. Littelmann)
Annals of Mathematics 155, 491--551 (2002). [pdf]
A conjectural generalization of the n! result to arbitrary groups (with J.F. Thomsen)
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Equivariant analogue of Grothendieck's theorem for vector bundles on \Bbb P^1
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The generalized triangle inequalities for rank 3 symmetric spaces of noncompact type (with B. Leeb and J. Millson)
Contemporary Mathematics vol. 332, published by AMS, 171--195 (2003). [pdf]
A new realization of the cohomology of Springer fibers (with J.F. Thomsen)
In: "Proceedings of the International Conference on Algebraic Groups and Arithmetic" (Volume dedicated to M.S. Raghunathan on his sixtieth birthday), Narosa Publishing House, 119--125 (2004). [pdf]
Induction functor in noncommutative equivariant cohomology and Dirac cohomology
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Explicit determination of the Picard group of moduli spaces of semi-stable G-bundles on curves (with A. Boysal)
Math. Annalen 332, 823--842 (2005). [pdf]
Extensions of algebraic groups (with K-H. Neeb)
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Eigenvalue problem and a new product in cohomology of flag varieties (with P. Belkale)
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On Cachazo-Douglas-Seiberg-Witten conjecture for simple Lie algebras
J. of Am. Math. Soc. 21, 797--808 (2008). [pdf]
The eigencone and saturation for Spin(8) (with M. Kapovich and J. Millson)
Pure and Applied Math. Quarterly 5, 755--780 (2009). [pdf]
Descent of line bundles to GIT quotients of flag varieties by maximal torus
Transformation Groups 13, 757--771 (2008). [pdf]
Special isogenies and tensor product multiplicities (with J. Stembridge)
International Mathematics Research Notices, vol. 2007 (no. 20), 1--13 (2007). [pdf]
Eigencone, saturation and Horn problems for symplectic and odd othogonal groups (with P. Belkale)
J. Alg. Geom. 19, 199--242 (2010). [pdf]
Characters of simplylaced nonconnected groups versus characters of nonsimplylaced connected groups (with G. Lusztig and D. Prasad)
Contemporary Math. vol. 478, 99--101 (2009). [pdf]
On positivity in T-equivariant K-theory of flag varieties (with W. Graham)
International Mathematical Research Notices, vol. 2008, 1--43 (August, 2008). [pdf]
A conjectural presentation of fusion algebras (with A. Boysal)
In: "Algebraic Analysis and Around" (in honor of M. Kashiwara's sixtieth birthday). Advanced Studies in Pure Mathematics vol. 54, 95--107 (2009). [pdf]
A generalization of Cachazo-Douglas-Seiberg-Witten conjecture for symmetric spaces
Math. Annalen 346, 67--84 (2010). [pdf]
Finiteness of the number of compatibly split subvarieties (with V. Mehta)
International Mathematics Research Notices, vol. 2009 (no. 19), 3595--3597 (2009). [pdf]
Tensor Product Decomposition
In: Proceedings of the International Congress of Mathematicians, Hyderabad, India, 2010. [pdf]
A generalization of Fulton's conjecture for arbitrary groups (with P. Belkale and N. Ressayre)
Math. Annalen 354, 401-425 (2012). [pdf]
Geometry of orbits of permanents and determinants
Comment. Math. Helv. 88, 759--788 (2013). [pdf]
An algebro-geometric realization of equivariant cohomology of some Springer fibers (with C. Procesi)
J. Algebra 368, 70--74 (2012). [pdf]
An approach towards the Kollar-Peskine problem via the Instanton Moduli Space
Proceedings of Symposia in Pure Mathematics 86, 217-225 (2012). [pdf]
Richardson varieties have Kawamata log terminal singularities (with K. Schwede)
International Mathematics Research Notices, rns241, (2012), 23 pages [pdf]
Positivity in T-Equivariant K-Theory of flag varieties associated to Kac-Moody groups
J. Eur. Math. Soc. 19, 2469--2519 (2017). [pdf]
A study of the representations supported by the orbit closure of the determinant
Compositio Math 151, 292-312 (2015). [pdf]
Dimension of zero weight space: an algebro-geometric approach (with D. Prasad)
J. Algebra 403, 324--344 (2014). [pdf]
A study of saturated tensor cone for symmetrizable Kac-Moody algebras (with M. Brown)
Math. Annalen 360, 901-936 (2014). [pdf]
A survey of the additive eigenvalue problem (with an appendix by M. Kapovich)
Transformation Groups 19, 1051-1148 (2014). [pdf]
Hitchin's conjecture for simply-laced Lie algebras implies that for any simple Lie algebra (with N. Bushek)
Differential Geometry and its Applications 35, 210--223 (2014). [pdf]
The multiplicative eigenvalue problem and deformed quantum cohomology (with P. Belkale)
Advances in Mathematics 288, 1309--1359 (2016). [pdf]
Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group (with J.M. Landsberg)
Discrete Mathematics 338, 1232--1238 (2015). [pdf]
Additive Eigenvalue Problem
EMS Newsletter (2015), 8 pages. [pdf]
Components of V(ρ) ⊗ V(ρ) (with R. Chirivi and A. Maffei)
Transformation Groups, 22, 645--650 (2017). [pdf]
Representation ring of Levi subgroups versus cohomology ring of flag varieties
Math. Annalen 366, 395--415 (2016). [pdf]
Positivity in T-equivariant K-theory of flag varieties associated to Kac-Moody groups II (with S. Baldwin)
Representation Theory (An electronic journal of the American Mathematical Society) 21, 35--60 (2017). [pdf]
A complete set of intertwiners for arbitrary tensor product representations via current algebras
Transformation Groups 24, 115--125 (2019). [pdf]
Conformal blocks for Galois covers of algebraic curves (with Jiuzu Hong), Preprint (2019), 72 pages.
[pdf]
On the faces of the tensor cone of symmetrizable Kac-Moody Lie algebras (with Nicolas Ressayre), Preprint (2019), 52 pages.
[pdf]
Eigenvalue problem for Hermitian matrices and its generalization to arbitrary reductive groups
(Talk given at AMS Sectional meeting held at Davidson College, March 2007) [pdf]
Geometry of Schubert varieties and Demazure character formula
(Talks given at the Hausdorff Research Institute for Mathematics, Bonn, Germany, April 2011) [pdf]
Borel-Weil-Bott theorem and geometry of Schubert varieties
(Lectures given at the MRC Meeting, Snowbird, Utah, June 2012) [pdf]
Equivariant K-theory of flag varieties
(Talks given at Jacobs University, Bremen (Germany), August 2012) [pdf]