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- W4297939408 abstract "First, we define a generalization of the standard quantum Toda chain inspired by a construction of quantum cohomology of partial flags spaces GL(ell+1)/P, P a parabolic subgroup. Common eigenfunctions of the parabolic quantum Toda chains are generalized Whittaker functions given by matrix elements of infinite-dimensional representations of gl(ell+1). For maximal parabolic subgroups (i.e. for P such that GL(ell+1)/P=mathbb{P}^{ell}) we construct two different representations of the corresponding parabolic Whittaker functions as correlation functions in topological quantum field theories on a two-dimensional disk. In one case the parabolic Whittaker function is given by a correlation function in a type A equivariant topological sigma model with the target space mathbb{P}^{ell}. In the other case the same Whittaker function appears as a correlation function in a type B equivariant topological Landau-Ginzburg model related with the type A model by mirror symmetry. This note is a continuation of our project of establishing a relation between two-dimensional topological field theories (and more generally topological string theories) and Archimedean (infty-adic) geometry. From this perspective the existence of two, mirror dual, topological field theory representations of the parabolic Whittaker functions provide a quantum field theory realization of the local Archimedean Langlands duality for Whittaker functions. The established relation between the Archimedean Langlands duality and mirror symmetry in two-dimensional topological quantum field theories should be considered as a main result of this note." @default.
- W4297939408 created "2022-10-01" @default.
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- W4297939408 date "2010-02-12" @default.
- W4297939408 modified "2023-09-25" @default.
- W4297939408 title "Parabolic Whittaker Functions and Topological Field Theories I" @default.
- W4297939408 doi "https://doi.org/10.48550/arxiv.1002.2622" @default.
- W4297939408 hasPublicationYear "2010" @default.
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