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# A path model for Whittaker vectors

* Corresponding author
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.
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Preprints, Working Papers, ...
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https://hal-cea.archives-ouvertes.fr/cea-01251620
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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

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1407.8423v1.pdf
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### Identifiers

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

### Citation

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

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