Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic integrability of Macdonald operators and representations of
  quantum groups   In this paper we construct examples of commutative rings of difference
operators with matrix coefficients from representation theory of quantum
groups, generalizing the results of our previous paper to the $q$-deformed
case. A generalized Baker-Akhiezer function $\Psi$ is realized as a matrix
character of a Verma module and is a common eigenfunction for a commutative
ring of difference operators. In particular, we obtain the following result in
Macdonald theory: at integer values of the Macdonald parameter $k$, there exist
difference operators commuting with Macdonald operators which are not
polynomials of Macdonald operators. This result generalizes an analogous result
of Chalyh and Veselov for the case $q=1$, to arbitrary $q$. As a by-product, we
prove a generalized Weyl character formula for Macdonald polynomials (a
conjecture by G.Felder and A.Varchenko), the duality for the $\Psi$-function,
and the existence of shift operators.

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The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th