Fetching the paper…
Reading the bibliography…
We show that the k-double Schur functions defined by the authors, and the quantum double Schubert polynomials studied by Kirillov and Maeno and by Ciocan-Fontanine and Fulton, can be obtained from each other by an explicit rational substitution.
B. Kostant, The solution to a generalized Toda lattice and representation theory. Adv. in Math. 34 (1979), no. 3, 195–338
1979
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.
V. Ginzburg, Perverse sheaves on a Loop group and Langlands’ duality, preprint, 1995; arXiv:alg-geom/9511007
1995
Earlier work this paper cites.
A. Givental and B. Kim. Quantum cohomology of flag manifolds and Toda lattices. Comm. Math. Phys. 168 (1995), no. 3, 609–641
1995
Earlier work this paper cites.
B. Kostant, Flag Manifold Quantum Cohomology, the Toda Lattice, and the Representation with Highest Weight. Selecta Mathematica, New Series 2 (1996), 43–91
1996
Earlier work this paper cites.
D. Peterson, Lecture notes at MIT, 1997
1997
Earlier work this paper cites.
I. Ciocan-Fontanine and W. Fulton, Quantum double Schubert polynomials. Appendix J in Schubert Varieties and Degeneracy Loci, Lecture Notes in Math. 1689(1998), 134–138
1998
Earlier work this paper cites.
B. Kim, Quantum Cohomology of Flag Manifolds G / B G/B and Quantum Toda Lattices. Ann. of Math. 149 (1999), 129–148
1999
Earlier work this paper cites.
A. N. Kirillov and T. Maeno, Quantum double Schubert polynomials, quantum Schubert polynomials and the Vafa-Intriligator formula, in Formal power series and algebraic combinatorics (Vienna, 1997). Discrete Math. 217 (2000), no. 1–3, 191–223,
2000
Cited alongside, same era.
A.-L. Mare, Polynomial representatives of Schubert classes in Q H ∗ ( G / B ) QH^{*}(G/B) . Math. Res. Lett. 9 (2002), no. 5-6, 757–769
2002
Cited alongside, same era.
A. Lascoux, L. Lapointe, and J. Morse, Tableau atoms and a new Macdonald positivity conjecture. Duke Math. J. 116 (2003), no. 1, 103–146
2003
Cited alongside, same era.
L. Mihalcea, Positivity in equivariant quantum Schubert calculus. Amer. J. Math. 128 (2006), no. 3, 787?803
2006
Cited alongside, same era.
P. Magyar, Notes on Schubert classes of a loop group, preprint, 2007; arXiv:0705.3826
Molev, Comultiplication rules for the double Schur functions and Cauchy identities. Electron. J. Combin. 16 (2009), no. 1, Research Paper 13, 44 pp
2009
Later among the works it cites.
Anderson and Chen, personal communication, 2010
2010
Later among the works it cites.
T. Lam and M. Shimozono, Quantum cohomology of G / P G/P and homology of affine Grassmannian. Acta. Math. 204 (2010), 49–90
2010
Later among the works it cites.
T. Lam, A. Schilling, and M. Shimozono, Schubert polynomials for the affine Grassmannian of the symplectic group. Math. Z. 264 (2010), no. 4, 765–811
2010
Later among the works it cites.
S. Pon, Affine Stanley Symmetric Functions for Classical Groups, Ph. D. thesis, University of California, Davis, 2010
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2007
Cited alongside, same era.
T. Lam, Schubert polynomials for the affine Grassmannian. J. Amer. Math. Soc. 21 (2008), no. 1, 259–281
2008
Cited alongside, same era.
K. Riestch. A mirror symmetric construction of q H T ∗ ( G / P ) ( q ) qH^{\ast}_{T}(G/P)_{(q)} . Adv. Math. 217 (2008), no. 6, 2401–2442
2008
Cited alongside, same era.
P.-E. Chaput, L. Manivel, and N. Perrin, Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces. Mathematical Research Letters, 16 (2009), 7–21
2009
Cited alongside, same era.
J. C. Brunson and M. Shimozono, k k -Schur functions as multidegrees of matrix affine Schubert varieties, in preparation
Cited in the paper.
N.C. Leung and C. Li, Gromov-Witten invariants for G/B and Pontryagin product for Ω K \Omega K . TAMS, to appear
Cited in the paper.
2011
Closest in time.