UCR
Dept of Mathematics

Home page of Jacob Greenstein

Last modified on February 27, 2008

Research interests

Lie algebras, quantum affine algebras, representation theory. I am one of 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 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 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 sl(l+1)^ 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.
  10. (with V. Chari) Current algebras, highest weight categories and quivers, Advances in Mathematics 216 (2007), no. 2, 811--840
  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

Teaching

MATH 009B Winter 2007 First year calculus, Part B.
MATH 201B Winter 2007 Graduate algebra, Part B: modules.
MATH 113 Fall 2006 Applied linear algebra
MATH 135A Fall 2006 Numerical Methods
MATH 172 Spring 2006 Modern algebra
MATH 226 Spring 2006 Lie algebras
MATH 113 Fall 2005 Applied linear algebra
MATH 009C Fall 2005 First year calculus, Part C
MATH 010A Spring 2005Calculus of several variables, Part A
MATH 046 Spring 2005Differential equations
MATH 131 Fall 2004Linear algebra
MATH 171 Fall 2004Introduction to modern algebra

Useful Links

TMR network "Algebraic Lie Representations"
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
USA
• Phone
+1 (951) 827 5098
• Fax:
+1 (951) 827 7314

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