4,916 research outputs found
Rarefied elliptic hypergeometric functions
Two exact evaluation formulae for multiple rarefied elliptic beta integrals
related to the simplest lens space are proved. They generalize evaluations of
the type I and II elliptic beta integrals attached to the root system . In
a special case, the simplest limit is shown to lead to a new
class of -hypergeometric identities. Symmetries of a rarefied elliptic
analogue of the Euler-Gauss hypergeometric function are described and the
respective generalization of the hypergeometric equation is constructed. Some
extensions of the latter function to and root systems and
corresponding symmetry transformations are considered. An application of the
rarefied type II elliptic hypergeometric function to some eigenvalue
problems is briefly discussed.Comment: 41 pp., corrected numeration of formula
Deformed Conformal and Supersymmetric Quantum Mechanics
Within the standard quantum mechanics a q-deformation of the simplest N=2
supersymmetry algebra is suggested. Resulting physical systems do not have
conserved charges and degeneracies in the spectra. Instead, superpartner
Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from
another by the q^2-factor scaling. A special class of the self-similar
potentials is shown to obey the dynamical conformal symmetry algebra su_q(1,1).
These potentials exhibit exponential spectra and corresponding raising and
lowering operators satisfy the q-deformed harmonic oscillator algebra of
Biedenharn and Macfarlane.Comment: 11 page
Elliptic hypergeometric terms
General structure of the multivariate plain and q-hypergeometric terms and
univariate elliptic hypergeometric terms is described. Some explicit examples
of the totally elliptic hypergeometric terms leading to multidimensional
integrals on root systems, either computable or obeying non-trivial symmetry
transformations, are presented.Comment: 20 pp., version to appear in a workshop proceeding
Aspects of elliptic hypergeometric functions
General elliptic hypergeometric functions are defined by elliptic
hypergeometric integrals. They comprise the elliptic beta integral, elliptic
analogues of the Euler-Gauss hypergeometric function and Selberg integral, as
well as elliptic extensions of many other plain hypergeometric and
-hypergeometric constructions. In particular, the Bailey chain technique,
used for proving Rogers-Ramanujan type identities, has been generalized to
integrals. At the elliptic level it yields a solution of the Yang-Baxter
equation as an integral operator with an elliptic hypergeometric kernel. We
give a brief survey of the developments in this field.Comment: 15 pp., 1 fig., accepted in Proc. of the Conference "The Legacy of
Srinivasa Ramanujan" (Delhi, India, December 2012
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