Mathematical Research Letters

Volume 19 (2012)

Number 1

From quantum Schubert polynomials to $k$-Schur functions via the Toda lattice

Pages: 81 – 93



Thomas Lam (Department of Mathematics, University of Michigan, 530 Church St., Ann Arbor, MI 48109, USA)

Mark Shimozono (Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA)


We show that Lapointe–Lascoux–Morse $k$-Schur functions (at $t=1$) and Fomin–Gelfand–Postnikov quantum Schubert polynomials can be obtained from each other by a rational substitution. This is based on Kostant’s solution of the Toda lattice and Peterson’s work on quantum Schubert calculus.

Full Text (PDF format)