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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 : Wednesday, April 14, 2021 - 12:12:08 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 : Wednesday, April 14, 2021 - 12:12:08 PM
Long-term archiving on: : Thursday, April 7, 2016 - 4:03:21 PM
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1407.8423v1.pdf
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