Homepage of Apoorva Khare

Contact information

Books; invited chapters/monographs in books

1. Mathematics in the Real World, with Anna Lachowska, forthcoming from Yale University Press.
2. Entry on the BGG Category O, for the Encyclopedia of Mathematics (Michiel Hazewinkel, Editor), Kluwer Academic Publishers, 2005.

Publications

1. Divisibility Tests, Furman University Electronic Journal of Undergraduate Mathematics FUEJUM Volume 3 (1997), pages 1-5.
2. Category O over a deformation of the symplectic oscillator algebra, Journal of Pure and Applied Algebra, Volume 195 No. 2 (January 2005), pages 131-166; erratum.
3. Category O over the symplectic oscillator algebra, Ph.D. Thesis, University of Chicago, June 2006.
4. Divisibility tests and recurring decimals in Euclidean domains (final section with Pieter Moree), JP Journal of Algebra, Number Theory, and Applications (JPANTA), Volume 7 No. 1 (February 2007), pages 1-32.
5. Quantized symplectic oscillator algebras of rank one, joint with Wee Liang Gan; Journal of Algebra Volume 310 No. 2 (April 2007), pages 671-707.
6. Vector spaces as unions of proper subspaces, Linear Algebra and its Applications Volume 431 No. 9 (1 October 2009), pages 1681--1686.
7. Functoriality of the BGG Category O, Communications in Algebra Volume 37 No. 12 (December 2009), pages 4431-4475.
8. Center and representations of infinitesimal Hecke algebras of sl_2, joint with Akaki Tikaradze, Communications in Algebra Volume 38 No. 2 (February 2010), pages 405-439.
9. Faces of weight polytopes and a generalization of a theorem of Vinberg, joint with Tim Ridenour, Algebras and Representation Theory Volume 15 No. 3 (June 2012), pages 593-611.
10. Faces of polytopes and Koszul algebras, joint with Vyjayanthi Chari and Tim Ridenour, Journal of Pure and Applied Algebra Volume 216 No. 7 (July 2012), pages 1611-1625.
11. Solutions of several coupled discrete models in terms of Lamé polynomials of arbitrary order, joint with Avinash Khare and Avadh Saxena, Pramana Volume 79 No. 3 (September 2012), pages 377-392.
12. The sum of a finite group of weights of a Hopf algebra, Axioms 1 No. 3 (October 2012), pages 259-290 (Special issue on: "Hopf Algebras, Quantum Groups and Yang-Baxter Equations").
13. Representations of complex semi-simple Lie groups and Lie algebras, in Connected at Infinity II: On the work of Indian mathematicians (R. Bhatia and C.S. Rajan, Eds.), Texts and Readings in Mathematics (TRIM), Hindustan Book Agency, 2013, pages 85-129. Here is the PDF.

Preprints

1. Faces and maximizer subsets of highest weight modules, math.RT/1301.1140. Here is the PDF.
   Here is a related announcement, where I compute 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.
2. Axiomatic framework for the BGG Category O; preprint, math.RT/0811.2080. Here is the PDF.
3. The covering problem for Chinese rings, preprint, math.AC/0906.1023. Here is the PDF.
4. Drinfeld-Hecke algebras over cocommutative algebras, preprint, math.RA/0705.2067. Here is the PDF.

Awards and support

• My research at Stanford is supported by a DARPA grant (DARPA YFA N66001-11-1-4131).

Conference Organization

• Lie Theory Workshop on Quantum Groups, Stanford University, February 4-5, 2012. Co-organized with Daniel Bump (Stanford) and Anne Schilling (UC Davis).
• Young Researchers Meet (Mathematics and Computer Science), Stanford University, May 26-27, 2012. Co-organizing with Govindan Rangarajan (Indian Institute of Science, India).