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.

Extension of a theorem of Kostant for affine algebras.
Journal of Algebra 199 (1998), no. 1, 290301.
(MR 99b:17031)

Characters of bounded $\widehat{\mathfrak{sl}(2)}$ modules.
Journal of Algebra 230 (2000), no. 2, 540–557.
(MR 2001m:17033)
 (with A. Joseph)
A ChevalleyKostant 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)
 (with V. Chari) Quantum loop modules.
Representation Theory 7, 56–80.
(MR
2004b:17044)

Characters of simple
bounded modules over an untwisted affine Lie algebra.
Algebras and Representation theory 6 (2003), no. 2, 119–137 (MR 2004c:17052)
 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)
 (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
 (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)
 (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)
 (with V. Chari) Current algebras, highest weight categories and quivers, Advances in Mathematics 216 (2007), no. 2, 811–840
(MR 2009d:17009)
 (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)
 (with V. Chari) A family of Koszul algebras arising from finitedimensional representations of simple Lie algebras, Advances in Mathematics 220 (2009), no. 4, 1193–1221 (MR 2010h:16067)
 Quivers with relations arising from Koszul algebras of $\mathfrak g$invariants, Journal of Algebra 322 (2009), no. 12, 4430–4478 (MR 2558871)
 (with V. Chari) Minimal affinizations as projective objects, Journal of Geometry and Physics 61 (2011), no. 3, 594–609 (MR2763623)
 (with A. Berenstein) Quantum folding, International Mathematics Research Notices 2011 (2011), no. 21, 4821–4883 (MR2852300)
 (with M. Bennett, V. Chari and N. Manning) On homomorphisms between global Weyl modules, Representation theory 15 (2011), 733–752 (MR2869017)
 (with A. Berenstein) Quantum Chevalley groups, Contemporary Mathematics
592 (2013), 71–102 (MR3087940 )
 (with A. Berenstein and D. Kazhdan) Integrable clusters, Comptes rendus de l'Académie de sciences (Mathématique) 353 (2015), no. 5, 387–390 (MR3334989)
 (with A. Berenstein) Generalized Joseph's decompositions, Comptes rendus de l'Académie de sciences (Mathématique) 353 (2015), no. 10, 887–892i (MR3411217)
 (with A. Berenstein) Primitively generated Hall algebras, Pacific Journal of Mathematics 281 (2016), no. 2, 287–331 (MR3463039)
 (with V. Mazorchuk) Koszul duality for semidirect products and generalized Takiff algebras, Algebras and Representation theory 20 (2017), no. 3, 675–694 (MR3651073)
 (with A. Berenstein) Double canonical bases, Advances in Mathematics 316 (2017), 381–468
 (with A. Berenstein) Canonical bases of quantum Schubert cells and their symmetries, Selecta Mathematica 23 (2017), no. 4, 2755–2799
 (with A. Berenstein and Jian Rong Li) On cacti and crystals (submitted)
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