 |
A path model for Whittaker vectors
Abstract : In this paper we construct weighted path models to compute Whittaker vectors in the completion of Verma modules, as well as Whittaker functions of fundamental type, for all finite-dimensional simple Lie algebras, affine Lie algebras, and the quantum algebra $U_q(\mathfrak{sl}_{r+1})$. This leads to series expressions for the Whittaker functions. We show how this construction leads directly to the quantum Toda equations satisfied by these functions, and to the $q$-difference equations in the quantum case. We investigate the critical limit of affine Whittaker functions computed in this way.
Cited literature [7 references]
https://hal-cea.archives-ouvertes.fr/cea-01251620
Contributor : Emmanuelle de Laborderie <>
Submitted on : Wednesday, January 6, 2016 - 2:59:31 PM
Last modification on : Monday, February 10, 2020 - 6:13:40 PM
Long-term archiving on: : Thursday, April 7, 2016 - 4:03:21 PM
Contributor : Emmanuelle de Laborderie <>
Submitted on : Wednesday, January 6, 2016 - 2:59:31 PM
Last modification on : Monday, February 10, 2020 - 6:13:40 PM
Long-term archiving on: : Thursday, April 7, 2016 - 4:03:21 PM
File
1407.8423v1.pdf
Files produced by the author(s)