Admissible sequences, preprojective representations of quivers, and reduced words in the weyl group of a Kac-Moody algebra

International Mathematics Research Notices

Volumn 2007, Issue , 2007, Pages

  Kleiner, Mark ^a   Pelley, Allen ^a  

^a SYRACUSE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36148949362     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rnm013     Document Type: Article

References (19)

1. Bernstein, I. N., I. M. Gelfand, and V. A. Ponomarev. "Coxeter Functors and Gabriel's Theorem." UspekhiMatematicheskikh Nauk 28 (1973): 19-33;
2. Transl. Russ. Math. Serv. 28 (1973): 17-32.
3. Auslander, M., I. Reiten, and S. O. Smalø. Representation Theory of Artin Algebras, Cambridge Studies in Advanced Mathematics. vol.36, New York: Cambridge University Press, 1994.
4. Kleiner, M., and H. R. Tyler. "Admissible Sequences and the Preprojective Component of a Quiver." Advances in Mathematics 192, no.2 (2005): 376-402.
5. Bourbaki, N. "Lie Groups and Lie Algebras." Pp. 1-300 in Elements of Mathematics (Berlin), Berlin: Springer-Verlag, 2002. Chapters 4-6 translated from the 1968 French original by Andrew Pressley.
6. Kac, V. G. Infinite-Dimensional Lie Algebras. 3rd ed. Cambridge: Cambridge University Press, 1990.
7. Howlett, R. B. "Coxeter Groups and M-Matrices." Bulletin of the London Mathematical Society 14, no.2 (1982): 137-141.
8. Fomin, S., and A. Zelevinsky. "Cluster Algebras IV: Coefficients." Compositio Mathematica 143, no.1 (2007): 112-164.
9. Dlab, V., and C.M. Ringel. "Indecomposable Representations of Graphs and Algebras." Memoirs of the American Mathematical Society 6, no.173 (1976): 1-57.
10. Kleiner, M., andH. R. Tyler. "Sequences of Reflection Functors and the PreprojectiveComponent of a Valued Quiver," (2006): Preprint arXiv:math.RT/0608175.
11. Krammer, D. The Conjugacy Problem of Coxeter Groups. Ph. D. Thesis, Universiteit Utrecht, 1994. Available at http://www.maths.warwick.ac.uk/~daan/.
12. Speyer, D. E. "Reduced Powers of Coxeter Elements," unpublishedmanuscript.
13. Reading,N. "Clusters, Coxeter-Sortable Elements and Noncrossing Partitions." Transactions of the American Mathematical Society (2005): Preprint arXiv:math.CO/0507186.
14. Fomin, S., and A. Zelevinsky. "Y-Systems and Generalized Associahedra." Annals of Mathematics (2) 158, no.3 (2003): 977-1018.
15. Marsh, R., M. Reineke, and A. Zelevinsky. "Generalized Associahedra via Quiver Representations." Transactions of the American Mathematical Society 355, no.10 (2003): 4171-4186.
16. McCammond, J. "Noncrossing Partitions in Surprising Locations." American Mathematical Monthly 113 (2006): 598-610.
17. Ringel, C.M. Tame Algebras and Integral Quadratic Forms, LectureNotes in Mathematics, vol.1099. Berlin: Springer-Verlag, 1984.
18. Dlab, V., and C. M. Ringel. "On Algebras of Finite Representation Type." Journal of Algebra 33 (1975): 306-394.
19. Ringel, C. M. "Green's theorem on Hall Algebras, Representation Theory of Algebras and Related Topics (Mexico City, 1994)." Pp. 185-245 in CMS Conference Proceedings, vol.19, Providence, RI: AmericanMathematical Society, 1996.