Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [7 references]  Display  Hide  Download
Contributor : Emmanuelle De Laborderie Connect in order to contact the contributor
Submitted on : Wednesday, January 6, 2016 - 2:59:31 PM
Last modification on : Monday, December 13, 2021 - 9:16:04 AM
Long-term archiving on: : Thursday, April 7, 2016 - 4:03:21 PM


Files produced by the author(s)


  • HAL Id : cea-01251620, version 1
  • ARXIV : 1407.8423


Philippe Di Francesco, R. Kedem, B. Turmunkh. A path model for Whittaker vectors. 2016. ⟨cea-01251620⟩



Record views


Files downloads