We characterize the law of the partition function of a Brownian directed polymer model in
terms of a diffusion process associated with the quantum Toda lattice. The proof is via a …

The concept of a Frobenius manifold was introduced by B. Dubrovin [9] to capture in an
axiomatic form the properties of correlators found by physicists (see [8]) in two-dimensional …

We define a toric degeneration of an integrable system on a projective manifold, and prove
the existence of a toric degeneration of the Gelfand–Cetlin system on the flag manifold of …

We show that the geometric lifting of the RSK correspondence introduced by AN Kirillov
(Physics and Combinatorics. Proc. Nagoya 2000 2nd Internat Workshop, pp. 82–150, 2001) …

The present paper proposes new integral representations of-Whittaker functions
corresponding to an arbitrary semisimple Lie algebra with the integrand expressed in terms …

We give two proofs of a conjecture of Hori and Vafa which expresses the J-function—a
generating function for 1-point descendant Gromov-Witten invariants—of a Grassmannian in …

Let G be a simple simply connected complex algebraic group. We give a Lie-theoretic
construction of a conjectural mirror family associated to a general flag variety G/P, and show …

Let Mk, m be the space of Laurent polynomials in one variable, where k, m≧ 1 are fixed
integers and. According to B. Dubrovin [B. Dubrovin, Geometry of 2d topological field …

Abstract Quantum Lefschetz theorem by Coates and Givental [T. Coates, AB Givental,
Quantum Riemann-Roch, Lefschetz and Serre, math. AG/0110142.] gives a relationship …

We interpret the equivariant cohomology algebra HGL n× C∗∗(T∗ F λ; C) of the cotangent
bundle of a partial flag variety F λ parametrizing chains of subspaces 0= F 0⊂ F 1⊂⋯⊂ FN …