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1.
Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U q (A 1 (1) ) and U q (A 2 (1) ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U q (A 1) and U q (A 2). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U q (A 2), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.  相似文献   

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3.
The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum groupU q(n). Thisq-BW construction uses a recursion procedure forU q(n) in which the fiber of the bundle carries an irrep ofU q(n–1)×U q(1) with sections that are holomorphic functions in the homogeneous spaceU q(n)/U q(n–1)×U q(1). Explicit results are obtained for theU q(n) irreps and for the related isomorphism of quantum group algebras.Supported in part by the National Science Foundation, No. PHY-9008007  相似文献   

4.
An algebra homomorphism from the nonstandard q-deformed (cyclically symmetric) algebra U q(so3) to the extension Û q(sl2) of the Hopf algebra U q(sl2) is constructed. Not all irreducible representations (IR) of U q(sl2) can be extended to representations of Û q(sl2). Composing the homomorphism with irreducible representations of Û q(sl2) we obtain representations of U q(so3). Not all of these representations of U q(so3) are irreducible. Reducible representations of U q(so3) are decomposed into irreducible components. In this way we obtain all IR of U q(so3) when q is not a root of unity. A part of these representations turn into IR of the Lie algebra so3 when q 1.  相似文献   

5.
It is shown that the quantum supergroup U q (osp(1/2n)) is essentially isomorphic to the quantum group U -q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.  相似文献   

6.
We construct the level one vertex operator representations of the q-deformation U q(B r (1) ) of the affine Kac-Moody algebra B r (1) . Beside the q-deformed vertex operators introduced by Frenkel and Jing, this construction involves a q-deformation of free fermionic fields.  相似文献   

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Nonstandard q-deformed algebras U q(so3) and U q(so4), which can be embedded into U q(sl3) and U q(sl4) and are coideals in them, are considered. It is shown how to multiply finite dimensional representations of U q(so3) when q is positive. Homomorphisms from U q(so3) and U q(so4) to the q-oscillator algebras are given. By making use of these homomorphisms, irreducible representations of U q(so3) and U q(so4) for q equal to a root of unity are obtained.  相似文献   

9.
We give an explicit formula for the vertex operators related to the level 1 representations of the quantum affine Lie algebrasU q (D n (1) ) in terms of bosons. As an application, we derive an integral formula for the correlation functions of the vertex models withU q (D n (1) )-symmetry.NJ was supported in part by NSA grant MDA904-93-H-3005 and University of Kansas General Research allocation.SJK was supported in part by Basic Science Research Institute Program, Ministry of Education of Korea, BSRI-94-1414 and GARC-KOSEF at Seoul National University, Korea.  相似文献   

10.
The structure of all discrete series of unitary irreducible representations of the U q (u(3, 1)) and U q (u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′) q . The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U q (u(n, 1)) ⊇ U q (u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra.  相似文献   

11.
The discrete series of unitary irreducible representations of the noncompact quantum algebra U q(2, 1) are studied. For the negative discrete series, two bases of these irreps are considered. One of them corresponds to the reduction U q(2, 1) → U q(2)×U(1). The second basis is connected with the reduction U q(2, 1) → U(1)×U q(1, 1). The matrix elements of the U q(2, 1) generators in both bases are calculated. For the intermediate discrete series, only first type of basis is considered and the q analogs of the Gelfand-Graev formulas are obtained. Also, the transformation brackets connecting the two bases are found for the negative discrete series.  相似文献   

12.
A general method is developed for constructing quantum group invariants and determining their eigenvalues. Applied to the universalR-matrix this method leads to the construction of a closed formula for link polynomials. To illustrate the application of this formula, the quantum groupsU q (E 8),U q (so(2m+1) andU q (gl(m)) are considered as examples, and corresponding link polynomials are obtained.  相似文献   

13.
We realize the Hopf algebraU q–1 (so(N)) as an algebra of differential operators on the quantum Euclidean spaceR q N . The generators are suitableq-deformed analogs of the angular momentum components on ordinaryR N . The algebra Fun(R q N ) of functions onR q N splits into a direct sum of irreducible vector representations ofU q–1 (so(N)); the latter are explicitly constructed as highest weight representations.  相似文献   

14.
We give explicit realization for the quantum enveloping algebras U q(B n). In these formulae the generators of the algebra are expressed by means of 2n–1 canonical q-boson pairs and one auxiliary representation of U q(B n–1)  相似文献   

15.
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU q(2) the Green function on the q-Podler's sphere M q = SU q(2)/U(1) is derived. Possible applications are briefly discussed.  相似文献   

16.
We write down a complete set of n-point Uq(sl(2)) invariants (using a polynomial basis for the irreducible finite dimensional U q -modules) that are regular for all nonzero values of the deformation parameter q.  相似文献   

17.
Operators of representations corresponding to symmetric elements of theq-deformed algebrasU q (su1,1),U q (so2,1),U q (so3,1),U q (so n ) and representable by Jacobi matrices are studied. Closures of unbounded symmetric operators of representations of the algebrasU q (su1,1) andU q (so2,1) are not selfadjoint operators. For representations of the discrete series their deficiency indices are (1,1). Bounded symmetric operators of these representations are trace class operators or have continuous simple spectra. Eigenvectors of some operators of representations are evaluated explicitly. Coefficients of transition to eigenvectors (overlap coefficients) are given in terms ofq-orthogonal polynomials. It is shown how results on eigenvectors and overlap coefficients can be used for obtaining new results in representation theory ofq-deformed algebras.  相似文献   

18.
The relation between the set of transformations of the quantum plane and the quantum universal enveloping algebra U q (u(2)) is investigated by constructing representations of the factor algebra U q (u(2))* . The noncommuting coordinates of , on which U q (2) * U q (2) acts, are realized as q-spinors with respect to each U q (u(2)) algebra. The representation matrices of U q (2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of directly from properties of U q (u(2)). The generalization of these results to U q (u(n)) and is also discussed.  相似文献   

19.
We give the Heisenberg realization for the quantum algebra U q (sl n ), which is written by theq-difference operator on the flag manifold. We construct it from the action of U q (sl n ) on theq-symmetric algebraA q (Mat n ) by the Borel-Weil-like approach. Our realization is applicable to the construction of the free field realization for U q [2].  相似文献   

20.
We characterize the finite-dimensional representations of the quantum affine algebra U q ( n+1) (whereq × is not a root of unity) which are irreducible as representations of U q (sl n+1). We call such representations small. In 1986, Jimbo defined a family of homomorphismsev a from U q (sl n+1) to (an enlargement of) U q (sl,n+1), depending on a parametera ·. A second family,ev a can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U q ( n+1) is obtained by pulling back an irreducible representation of U q (sl n+1) byev a orev a for somea ·.  相似文献   

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