Zobrazeno 1 - 10
of 503
pro vyhledávání: '"Klimyk, A."'
Autor:
Klimyk, Anatoly, Patera, Jiri
We define and study multivariate exponential functions, symmetric with respect to the alternating group A_n, which is a subgroup of the permutation (symmetric) group S_n. These functions are connected with multivariate exponential functions, determin
Externí odkaz:
http://arxiv.org/abs/0907.0601
Autor:
Klimyk, Anatoliy U., Patera, Jiri
Publikováno v:
SIGMA 4 (2008), 002, 57 pages
We review and further develop the theory of $E$-orbit functions. They are functions on the Euclidean space $E_n$ obtained from the multivariate exponential function by symmetrization by means of an even part $W_{e}$ of a Weyl group $W$, corresponding
Externí odkaz:
http://arxiv.org/abs/0801.0822
We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bounded, whereas the spectra of position and momentum are a denumerable non-degenerate set of points in [-1,1] that depends on the deformation param
Externí odkaz:
http://arxiv.org/abs/0711.3089
Autor:
Klimyk, A., Patera, J.
Publikováno v:
J. Math. Phys., vol. 48 (2007), 093504, 24 pages
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine
Externí odkaz:
http://arxiv.org/abs/0705.4186
Autor:
Klimyk, A., Patera, J.
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of t
Externí odkaz:
http://arxiv.org/abs/0705.3572
Autor:
Kachuryk, Ivan, Klimyk, Anatoliy
Publikováno v:
SIGMA 3 (2007), 055, 84 pages
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of kinematical parts
Externí odkaz:
http://arxiv.org/abs/math-ph/0703080
Autor:
Iorgov, N. Z., Klimyk, A. U.
Publikováno v:
Int. J. Math. Math. Sci. vol.2005, No.2 (2005), 225-262
The aim of this paper is to give a complete classification of irreducible finite dimensional representations of the nonstandard q-deformation U'_q(so(n)) (which does not coincide with the Drinfeld-Jimbo quantum algebra U_q(so(n)) of the universal env
Externí odkaz:
http://arxiv.org/abs/math/0702482
Autor:
Klimyk, Anatoliy, Patera, Jiri
Publikováno v:
SIGMA 3 (2007), 023, 83 pages
In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl group, corre
Externí odkaz:
http://arxiv.org/abs/math-ph/0702040
Autor:
Atakishiyev, M. N., Klimyk, A. U.
We argue that a customary q-difference equation for the continuous q-Hermite polynomials H_n(x|q) can be written in the factorized form as (D_q^2 - 1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference operator. This means th
Externí odkaz:
http://arxiv.org/abs/math/0602375
Autor:
Klimyk, Anatoliy, Patera, Jiri
Publikováno v:
SIGMA 2 (2006), 006, 60 pages
In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space $E_n$ are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diag
Externí odkaz:
http://arxiv.org/abs/math-ph/0601037