Home page of Jacob Greenstein

Last modified on April 6, 2018

Research interests

Lie algebras, quantum affine algebras, quantum group, representation theory. I am one of the organizers of the "Lie Theory" seminar.

Publications and preprints

  1. Extension of a theorem of Kostant for affine algebras. Journal of Algebra 199 (1998), no. 1, 290--301. (MR 99b:17031)
  2. Characters of bounded $\widehat{\mathfrak{sl}(2)}$ modules. Journal of Algebra 230 (2000), no. 2, 540–557. (MR 2001m:17033)
  3. (with A. Joseph) A Chevalley-Kostant presentation of basic modules for $\widehat{\mathfrak{sl}(2)}$ and the associated affine KPRV determinants at $q=1$. Bulletin des Sciences mathématiques 125 (2001), no. 2, 85–108. (MR 2002c:17006)
  4. (with V. Chari) Quantum loop modules. Representation Theory 7, 56–80. (MR 2004b:17044)
  5. Characters of simple bounded modules over an untwisted affine Lie algebra. Algebras and Representation theory 6 (2003), no. 2, 119–137 (MR 2004c:17052)
  6. Littelmann's path crystal and combinatorics of certain integrable $\widehat{\mathfrak{sl}_{\ell+1}}$-modules of level zero. Journal of Algebra 269 (2003), no. 1, 347–372 (MR 2004j:17033)
  7. (with P. Lamprou) Path model for quantum loop modules of fundamental type. International Mathematics Research Notices 2004 (2004), no. 14, 675–711 (MR 2004m:17033
  8. (with V. Chari) Filtrations and completions of certain positive level modules of affine algebras. Advances in Mathematics 194 (2005), no. 2, 296–331 (MR 2006e:17018)
  9. (with V. Chari) An application of free Lie algebras to polynomial current algebras and their representation theory. Contemporary Mathematics 392 (2005), 15–31 (MR 2007b:17037)
  10. (with V. Chari) Current algebras, highest weight categories and quivers, Advances in Mathematics 216 (2007), no. 2, 811–840 (MR 2009d:17009)
  11. (with V. Chari) Graded level zero integrable representations of affine Lie algebras, Transactions of the American Mathematical Society 360 (2008), no. 6, 2923–2940 (MR 2009d:17033)
  12. (with V. Chari) A family of Koszul algebras arising from finite-dimensional representations of simple Lie algebras, Advances in Mathematics 220 (2009), no. 4, 1193–1221 (MR 2010h:16067)
  13. Quivers with relations arising from Koszul algebras of $\mathfrak g$-invariants, Journal of Algebra 322 (2009), no. 12, 4430–4478 (MR 2558871)
  14. (with V. Chari) Minimal affinizations as projective objects, Journal of Geometry and Physics 61 (2011), no. 3, 594–609 (MR2763623)
  15. (with A. Berenstein) Quantum folding, International Mathematics Research Notices 2011 (2011), no. 21, 4821–4883 (MR2852300)
  16. (with M. Bennett, V. Chari and N. Manning) On homomorphisms between global Weyl modules, Representation theory 15 (2011), 733–752 (MR2869017)
  17. (with A. Berenstein) Quantum Chevalley groups, Contemporary Mathematics 592 (2013), 71–102 (MR3087940 )
  18. (with A. Berenstein and D. Kazhdan) Integrable clusters, Comptes rendus de l'Académie de sciences (Mathématique) 353 (2015), no. 5, 387–390 (MR3334989)
  19. (with A. Berenstein) Generalized Joseph's decompositions, Comptes rendus de l'Académie de sciences (Mathématique) 353 (2015), no. 10, 887–892i (MR3411217)
  20. (with A. Berenstein) Primitively generated Hall algebras, Pacific Journal of Mathematics 281 (2016), no. 2, 287–331 (MR3463039)
  21. (with V. Mazorchuk) Koszul duality for semidirect products and generalized Takiff algebras, Algebras and Representation theory 20 (2017), no. 3, 675–694 (MR3651073)
  22. (with A. Berenstein) Double canonical bases, Advances in Mathematics 316 (2017), 381–468
  23. (with A. Berenstein) Canonical bases of quantum Schubert cells and their symmetries, Selecta Mathematica 23 (2017), no. 4, 2755–2799
  24. (with A. Berenstein and Jian Rong Li) On cacti and crystals (submitted)


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Useful Links

Mathematical Sciences Research Institute
American Mathematical Society European Mathematical Society
MathSciNet (mirrors in Houston, TX, Bielefeld, Germany and Strasbourg, France)
Journal of Algebra Journals published by Elsevier Science
Journals published by Springer Verlag arXiv.org e-Print archive
Mathematics Information Servers Mathematics Journals
The World Wide Web Consortium Google search engine

How to contact me

• E-mail:
jacob.greenstein at ucr.edu
• Snail mail:
Surge building, office 250
Department of Mathematics
University of California Riverside
Riverside CA 92521-0135
• Phone
+1 (951) 827 5098
• Fax:
+1 (951) 827 7314

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