Total positivity in Schubert varieties

Commentarii Mathematici Helvetici

Volumn 72, Issue 1, 1997, Pages 128-166

  Berenstein, Arkady ^a   Zelevinsky, Andrei ^b  

^a Department of Molecular Biology and Genetics   (United States)

^b NORTHEASTERN UNIVERSITY   (United States)

Author keywords

Bruhat decomposition; Schubert varieties; Semisimple Lie groups; Total positivity

Indexed keywords

EID: 0031459270     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00000363     Document Type: Article

References (11)

1. A. Berenstein, Group-like elements in quantum groups and Feigin's conjecture, 1996.
2. A. Berenstein, S. Fomin and A. Zelevinsky, Parametrizations of canonical bases and totally positive matrices, Adv. in Math. 122 (1996), 49-149.
3. N. Bourbaki, Groupes et algèbres de Lie, Ch. IV-VI, Hermann, Paris 1968.
4. N. Bourbaki, Groupes et algèbres de Lie, Ch. VII-VIII, Hermann, Paris 1975.
5. W. Fulton and J. Harris, Representation theory, Springer-Verlag, New York 1991.
6. J. E. Humphreys, Reflection groups and Coxeter groups, Cambridge University Press, Cambridge 1994.
7. B. Leclerc and A. Zelevinsky, Quasicommuting families of quantum Plücker coordinates, preprint, Université de Caen, Caen 1996.
8. G. Lusztig, Introduction to quantized enveloping algebras. In: J. Tirao, N. Wallach (Eds.), Progr. in Math. 105, Birkhäuser, Boston 1992, 49-65.
9. G. Lusztig, Introduction to quantum groups, Birkhäuser, Boston 1993.
10. G. Lusztig, Total positivity in reductive groups, in: Lie theory and geometry: in honor of Bertram Kostant, Progress in Mathematics 123, Birkhäuser, Boston 1994.
11. G. Lusztig, Total positivity and canonical bases, preprint.