One-dimensional nil-DAHA and Whittaker functions I

Details One-dimensional nil-DAHA and Whittaker functions I One-dimensional nil-DAHA and Whittaker functions I

2011-04-20

arxiv.org/abs/1104.3918v2

Mathematics

Quantum Algebra

v2: 4 references added, editing

Scientific paper

This paper is devoted primarily to the theory of Nil-DAHA for the root system A_1 and its applications to symmetric and spinor (nonsymmetric) global q-Whittaker functions. One of the main algebraic developments is an interpretation of the spinor-polynomial representation (introduced by the first author) as an induced module for the core subalgebra of Nil-DAHA, which provides the rasing and lowering operators for the q-Hermite polynomials. Analytically, the explicit Harish-Chandra-type asymptotic decomposition of global spherical and Whittaker functions seems the most interesting. The formula for the global Whittaker functions directly results from the theory of the core subalgebra.

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