Fetching the paper…
Reading the bibliography…
The totally nonnegative part of a partial flag variety G/P has been shown by the first author to be a union of semi-algebraic cells.
D. Kazhdan and G. Lusztig, Schubert varieties and Poincaré duality , Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203. MR 84g:14054
1980
Earlier work this paper cites.
V. Deodhar, On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells , Invent. Math. 79
1985
Earlier work this paper cites.
G. Lusztig, Canonical bases arising from quantized enveloping algebras , J. Amer. Math. Soc. 3 (1990), 447–498
1990
Earlier work this paper cites.
W. Fulton, Introduction to toric varieties , Ann. Math. Studies, 131
1993
Earlier work this paper cites.
by same author, Introduction to Quantum Groups, Progr. in Math. 110, Birkhauser Boston, 1993, 341 pages
1993
Earlier work this paper cites.
by same author, Total positivity in reductive groups , Lie theory and geometry: in honor of Bertram Kostant (G. I. Lehrer, ed.), Progress in Mathematics, vol. 123, Birkhaeuser, Boston, 1994, pp. 531–568
1994
Earlier work this paper cites.
by same author, Introduction to total positivity , Positivity in Lie theory: open problems, de Gruyter Exp. Math., vol. 26, de Gruyter, Berlin, 1998, pp. 133–145. MR MR1648700 (99h:20077)
1998
Cited alongside, same era.
by same author, Total positivity in partial flag manifolds , Representation Theory 2
1998
Cited alongside, same era.
by same author, Total positivity and real flag varieties , Ph.D. thesis, M.I.T., 1998
1998
Cited alongside, same era.
T. A. Springer, Linear algebraic groups, Second edition , Progress in Mathematics, vol. 9, Birkhäuser, Boston, 1998
1998
Cited alongside, same era.
by same author, An algebraic cell decomposition of the nonnegative part of a flag variety , J. Algebra 213
1999
Cited alongside, same era.
D. Cox, What is a toric variety? Topics in algebraic geometry and geometric modeling , Contemp. math., 334
2003
Later among the works it cites.
F. Sottile, Toric ideals, real toric varieties, and the moment map , in Topics in Algebraic Geometry and Geometric Modeling, Contemp. Math. 334
2003
Later among the works it cites.
R. J. Marsh and K. Rietsch, Parametrizations in flag varieties , Representation Theory 8
2004
Later among the works it cites.
M. Nanba, Bruhat order on the fixed-point subgroup by a Coxeter graph automorphism , J. Algebra 285
2005
Later among the works it cites.
by same author, Closure relations for totally nonnegative cells in G/P , Mathematical Research Letters 13
2006
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Berenstein, A. Zelevinsky, Tensor product multiplicities, canonical bases and totally positive varieties , Invent. math., 143
2001
Cited alongside, same era.
D. Cox, Minicourse on Toric varieties , http://www.amherst.edu/ dacox
Cited in the paper.
A. Postnikov, Total positivity, Grassmannians, and networks . arXiv:math.CO/0609184
Cited in the paper.
A. Postnikov, D. Speyer, and L. Williams, Matching polytopes, toric geometry, and the non-negative part of the Grassmannian , arXiv:math.AG/0706.2501
Cited in the paper.
K. Rietsch, A mirror symmetric construction for q H T ∗ ( G / P ) q{H}_{T}^{*}({G}/{P}) , math.AG/0511124, to appear in Adv. Math
Cited in the paper.
2007
Later among the works it cites.