Quantum double Schubert polynomials represent Schubert classes

A. Borel, Sur la cohomologie des espaces fibés principaux et des espaces homogènes des groupes de Lie compacts. Ann. of Math. (2) 57 (1953), 115–207

1953

Earlier work this paper cites.

D. Monk, The geometry of flag manifolds. Proc. London Math. Soc. (3) 9 (1959), 253–286

1959

Earlier work this paper cites.

I.N. Bernstein, I.M. Gelfand, and S.I. Gelfand, Schubert cells and the cohomology of a flag space. (Russian) Funkcional. Anal. i Priložen. 7 (1973), no. 1, 64–65

1973

Earlier work this paper cites.

A. Lascoux and M.-P. Schützenberger, Symmetry and flag manifolds, Lecture Notes in Mathematics 996 (1983) 118–144

1983

Earlier work this paper cites.

B. Kostant and S. Kumar, The nil Hecke ring and cohomology of G / P G/P for a Kac-Moody group G G . Adv. in Math. 62 (1986), no. 3, 187–237

1986

Earlier work this paper cites.

J.E. Humphreys, Reflection groups and Coxeter groups. Cambridge Studies in Advanced Mathematics, 29. Cambridge University Press, Cambridge, 1990. xii+204 pp

1990

Earlier work this paper cites.

I. G. Macdonald, Schubert polynomials. Surveys in combinatorics, 1991 (Guildford, 1991), 73–99, London Math. Soc. Lecture Note Ser., 166, Cambridge Univ. Press, Cambridge, 1991

1991

Earlier work this paper cites.

C. Chevalley, Sur les décompositions cellulaires des espaces G / B G/B in Algebraic Groups and their Generalizations: Classical Methods, American Mathematical Society, 1994, pp. 1-23. Proceedings and Symposia in Pure Mathematics, vol. 56, Part 1

1994

Earlier work this paper cites.

A. Astashkevich and V. Sadov, Quantum cohomology of partial flag manifolds. Comm. Math. Phys. 170 (1995), 503-528

1995

Earlier work this paper cites.

I. Ciocan-Fontanine, Quantum cohomology of flag varieties. Intern. Math. Research Notices (1995), no. 6, 263–277

1995

Cited alongside, same era.

A. Givental and B. Kim, Quantum cohomology of flag manifolds and Toda lattices. Comm. Math. Phys. 168 (1995), no. 3, 609–641

1995

Cited alongside, same era.

B. Kim, Quantum cohomology of partial flag manifolds and a residue formula for their intersection pairings. Internat. Math. Res. Notices 1995, no. 1, 1–15 (electronic)

1995

Cited alongside, same era.

B. Kim, On equivariant quantum cohomology. Internat. Math. Res. Notices 1996, no. 17, 841–851

1996

Cited alongside, same era.

S. Fomin, S.I. Gelfand, and A. Postnikov, Quantum Schubert polynomials. J. Amer. Math. Soc. 10 (1997), no. 3, 565–596

1997

Cited alongside, same era.

B. Kim, Quantum cohomology of flag manifolds G / B G/B and quantum Toda lattices. Ann. of Math. (2) 149 (1999), no. 1, 129–148

1999

Later among the works it cites.

A.N. Kirillov and T. Maeno, Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Formal power series and algebraic combinatorics (Vienna, 1997). Discrete Math. 217 (2000), no. 1-3, 191–223

2000

Later among the works it cites.

S.A. Robinson, Equivariant Schubert calculus. Thesis (Ph.D.) The University of North Carolina at Chapel Hill. 2001. 49 pp

2001

Later among the works it cites.

W. Fulton and C. Woodward, On the quantum product of Schubert classes. J. Algebraic Geom. 13 (2004), no. 4, 641–661

2004

Later among the works it cites.

D. Anderson, Double Schubert polynomials and double Schubert varieties, preprint, 2006

2006

Later among the works it cites.