Point-to-line polymers and orthogonal Whittaker functions

@article{Bisi2019PointtolinePA,
  title={Point-to-line polymers and orthogonal Whittaker functions},
  author={Elia Bisi and Nikos Zygouras},
  journal={Transactions of the American Mathematical Society},
  year={2019}
}
We study a one-dimensional directed polymer model in an inverse-gamma random environment, known as the log-gamma polymer, in three different geometries: point-to-line, point-to-half-line and when the polymer is restricted to a half-space with end point lying free on the corresponding half-line. Via the use of A. N. Kirillov's geometric Robinson-Schensted-Knuth correspondence, we compute the Laplace transform of the partition functions in the above geometries in terms of orthogonal Whittaker… 

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