Czechoslovak Journal of Physics - CZECH J PHYS, 2000
The nonstandard q-deformation Uq(son) of the universal enveloping algebra U(so n ) has irreducibl... more The nonstandard q-deformation Uq(son) of the universal enveloping algebra U(so n ) has irreducible finite dimensional representations which are a q-deformation of the well-known irreducible finite dimensional representations of U(so n ). But U'q(son) also has irreducible finite dimensional representations which have no classical analogue. The aim of this paper is to give these representations which are called nonclassical type representations. They are given by explicit formulas for operators of the representations corresponding to the generators of U'q(son).
The nonstandard q-deformed algebras U'_q(so_n) are known to possess q-analogues of Gel'... more The nonstandard q-deformed algebras U'_q(so_n) are known to possess q-analogues of Gel'fand-Tsetlin type representations. For these q-algebras, all the Casimir elements (corresponding to basis set of Casimir elements of so(n)) are found, and their eigenvalues within irreducible representations are given explicitly.
The aim of this paper is to announce the results on irreducible nonclassical type representations... more The aim of this paper is to announce the results on irreducible nonclassical type representations of the nonstandard q-deformations U'_q(so_n), U_q(iso_n) and U'_q(so_{n,1}) of the universal enveloping algebras of the Lie algebras so(n,C), iso_n and so_{n,1} when q is a real number (the algebra U'_q(so_{n,1}) is a real form of the algebra U'_q(so_{n+1})). These representations are characterized by the properties that they are singular at the point q=1.
Czechoslovak Journal of Physics - CZECH J PHYS, 2000
The nonstandard q-deformation Uq(son) of the universal enveloping algebra U(so n ) has irreducibl... more The nonstandard q-deformation Uq(son) of the universal enveloping algebra U(so n ) has irreducible finite dimensional representations which are a q-deformation of the well-known irreducible finite dimensional representations of U(so n ). But U'q(son) also has irreducible finite dimensional representations which have no classical analogue. The aim of this paper is to give these representations which are called nonclassical type representations. They are given by explicit formulas for operators of the representations corresponding to the generators of U'q(son).
The nonstandard q-deformed algebras U'_q(so_n) are known to possess q-analogues of Gel'... more The nonstandard q-deformed algebras U'_q(so_n) are known to possess q-analogues of Gel'fand-Tsetlin type representations. For these q-algebras, all the Casimir elements (corresponding to basis set of Casimir elements of so(n)) are found, and their eigenvalues within irreducible representations are given explicitly.
The aim of this paper is to announce the results on irreducible nonclassical type representations... more The aim of this paper is to announce the results on irreducible nonclassical type representations of the nonstandard q-deformations U'_q(so_n), U_q(iso_n) and U'_q(so_{n,1}) of the universal enveloping algebras of the Lie algebras so(n,C), iso_n and so_{n,1} when q is a real number (the algebra U'_q(so_{n,1}) is a real form of the algebra U'_q(so_{n+1})). These representations are characterized by the properties that they are singular at the point q=1.
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Papers by Nikolai Iorgov