Affiliation | Research Associate (joint in Mathematics and Statistics), Stanford University |
Office |
Littlefield Center, Room 334 |
Postal address |
Sequoia Hall, 390 Serra Mall, Stanford, CA - 94305 |
Phone |
650-723-2957 (Office) |
Fax |
650-725-8977 (Office) |
khare AT university-name DOT edu | |
Ph.D. | University of Chicago |
1 | Beautiful, Simple, Exact, Crazy: Mathematics in the Real World
(480 pp., with Anna Lachowska)
Yale University Press, 2015. See here for more information on the course which I developed and taught in Spring 2011 at Yale, and which led to the book. (The book title is inspired from a talk by Israel Moiseevich Gelfand.) |
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2 | Entry on the BGG Category O, for the Encyclopedia of Mathematics (Michiel Hazewinkel, Editor), Kluwer Academic Publishers. |
18 | Standard parabolic subsets of highest weight modules
Transactions of the American Mathematical Society, in press. |
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17 | Representations of complex semi-simple Lie groups and Lie
algebras
Connected at Infinity II: A Selection of Mathematics by Indians (R. Bhatia, C.S. Rajan, and A.I. Singh, Eds.), Texts and Readings in Mathematics (TRIM), Hindustan Book Agency (2013), pages 85-129. |
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16 | Faces of polytopes and Koszul algebras (with Vyjayanthi Chari
and Tim Ridenour)
Journal of Pure and Applied Algebra 216 No. 7 (2012), pages 1611-1625. |
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15 | Faces of weight polytopes and a generalization of a theorem of
Vinberg (with Tim Ridenour)
Algebras and Representation Theory 15 No. 3 (2012), pages 593-611. |
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14 | The sum of a finite group of weights of a Hopf algebra
Axioms 1 No. 3 (2012), pages 259-290 (Special issue on: "Hopf Algebras, Quantum Groups and Yang-Baxter Equations"). |
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13 | Solutions of several coupled discrete models in terms of
Lamé polynomials of arbitrary order
(with Avinash Khare and Avadh Saxena)
Pramana 79 No. 3 (2012), pages 377-392. |
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12 | Center and representations of infinitesimal Hecke algebras of
$\mathfrak{sl}_2$ (with Akaki Tikaradze)
Communications in Algebra 38 No. 2 (2010), pages 405-439. |
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11 | Functoriality of the BGG Category $\mathcal{O}$
Communications in Algebra 37 No. 12 (2009), pages 4431-4475. |
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10 | Vector spaces as unions of proper subspaces
Linear Algebra and its Applications 431 No. 9 (2009), pages 1681-1686. |
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9 | Quantized symplectic oscillator algebras of rank one
(with Wee Liang Gan)
Journal of Algebra 310 No. 2 (2007), pages 671-707. |
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8 | Divisibility tests and recurring decimals in Euclidean domains
(final section with Peter Moree)
JP Journal of Algebra, Number Theory, and Applications (JPANTA) 7 No. 1 (2007), pages 1-32. |
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7 | Category $\mathcal{O}$ over a deformation of the symplectic
oscillator algebra
Journal of Pure and Applied Algebra 195 No. 2 (2005), pages 131-166; erratum. |
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6 | Divisibility tests
Furman University Electronic Journal of Undergraduate Mathematics (FUEJUM) 3 (1997), pages 1-5. |
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5 | On Category $\mathcal{O}$ over triangular Generalized Weyl
Algebras (with Akaki Tikaradze)
Preprint, 2015. |
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4 | Axiomatic framework for the BGG Category $\mathcal{O}$
Preprint, 2015 (updated with major revisions from an earlier version). |
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3 | Faces and maximizer subsets of highest weight modules
Preprint, 2013. Here is a related announcement, which computes the weights of all simple highest weight modules (and others) over a complex semisimple Lie algebra: Weights of simple highest weight modules over a complex semisimple Lie algebra, math.RT/1305.4104. |
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2 | The covering problem for Chinese rings
Preprint (under revision), 2009. |
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1 | Drinfeld-Hecke algebras over cocommutative algebras
Preprint (under revision), 2007. |