Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral extension of the quantum group cotangent bundle   The structure of a cotangent bundle is investigated for quantum linear groups
GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we
construct an extension of the algebra of differential operators on SLq(n)
(otherwise called the Heisenberg double) by spectral values of the matrix of
right invariant vector fields. We consider two applications for the spectral
extension. First, we describe the extended Heisenberg double in terms of a new
set of generators -- the Weyl partners of the spectral variables. Calculating
defining relations in terms of these generators allows us to derive SLq(n) type
dynamical R-matrices in a surprisingly simple way. Second, we calculate an
evolution operator for the model of q-deformed isotropic top introduced by
A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we
present two possible expressions for it. The first one is a Riemann theta
function in the spectral variables. The second one is an almost free motion
evolution operator in terms of logarithms of the spectral variables. Relation
between the two operators is given by a modular functional equation for Riemann
theta function.

34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org