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This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations of their a
Externí odkaz:
http://arxiv.org/abs/1911.08767
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se
Externí odkaz:
http://arxiv.org/abs/1907.01281
This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3,2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hil
Externí odkaz:
http://arxiv.org/abs/1802.08497
Autor:
Celeghini, E., del Olmo, M. A.
A ladder algebraic structure for $L^2(\mathbb{R}^+)$ which closes the Lie algebra $h(1)\oplus h(1)$, where $h(1)$ is the Heisenberg-Weyl algebra, is presented in terms of a basis of associated Laguerre polynomials. Using the Schwinger method the quad
Externí odkaz:
http://arxiv.org/abs/1702.02003
We study here the generalized Weimar-Woods contractions of the superalgebra $osp(1|32) \oplus osp(1|32)$ in order to obtain a suitable algebra that could describe the gauge group of $D=11$ supergravity. The contracted superalgebras are assumed to be
Externí odkaz:
http://arxiv.org/abs/1504.05946
Akademický článek
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A symmetry $SU(2,2)$ group in terms of ladder operators is presented for the Jacobi polynomials, $J_{n}^{(\alpha,\beta)}(x)$, and the Wigner $d_j$-matrices where the spins $j=n+(\alpha+\beta)/2$ integer and half-integer are considered together. A uni
Externí odkaz:
http://arxiv.org/abs/1402.5217
A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir C_SU(2,2)=-3/2. As t
Externí odkaz:
http://arxiv.org/abs/1307.7380
Autor:
Celeghini, E., del Olmo, M. A.
A ladder structure of operators is presented for the associated Legendre polynomials and the spherical harmonics showing that both belong to the same irreducible representation of so(3,2). As both are also bases of square-integrable functions, the un
Externí odkaz:
http://arxiv.org/abs/1210.5192
Autor:
Gazeau, J. P., del Olmo, M. A.
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0< q < 1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure.
Externí odkaz:
http://arxiv.org/abs/1207.1200