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1.
A quantum analogue of the dual pair
is introduced in terms of the oscillator representation of U
q
. Its commutant and the associated identity of Capelli type are discussed. 相似文献
2.
Let
be a finite-dimensional complex simple Lie algebra and Uq(
) the associated quantum group (q is a nonzero complex number which we assume is transcendental). IfV is a finitedimensional irreducible representation of Uq(
), an affinization ofV is an irreducible representationVV of the quantum affine algebra Uq(
) which containsV with multiplicity one and is such that all other irreducible Uq(
)-components ofV have highest weight strictly smaller than the highest weight ofV. There is a natural partial order on the set of Uq(
) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) if
is of typeA, B, C, F orG, the minimal affinization is unique up to Uq(
)-isomorphism; (ii) if
is of typeD orE and is not orthogonal to the triple node of the Dynkin diagram of
, there are either one or three minimal affinizations (depending on ). In this paper, we show, in contrast to the regular case, that if Uq(
) is of typeD
4 and is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of .As a by-product of our methods, we disprove a conjecture according to which, if
is of typeA
n,every affinization is isomorphic to a tensor product of representations of Uq(
) which are irreducible under Uq(
) (in an earlier paper, we proved this conjecture whenn=1).Both authors were partially supported by the NSF, DMS-9207701. 相似文献
3.
We define and calculate the fusion algebra of a WZW model at a rational level using cohomological methods. As a byproduct, we obtain a cohomological characterization of admissible representations of
2. 相似文献
4.
Ruedi Suter 《Communications in Mathematical Physics》1994,163(2):359-393
The restricted quantum universal enveloping algebra
decomposes in a canonical way into a direct sum of indecomposable left (or right) ideals. They are useful for determining the direct summands which occur in the tensor product of two simple
. The indecomposable finite-dimensional
are classified and located in the Auslander-Reiten quiver. 相似文献
5.
Covariant differential calculi on the quantum space
for the quantum group SL
q
(2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de
j
of the generators of
form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), there exists a unique differential calculus with the above properties on the space
which corresponds to Podles' quantum sphereS
qc
/2
. 相似文献
6.
This Letter concerns an extension of the quantum spinor construction of
. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, and construct quantum spinor representations of
. 相似文献
7.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let
be a fixed Lie algebra. We shall say that a Kontsevich star product is
-relative if, on
*, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if
is a semi-simple Lie algebra, the only strict Kontsevich
-relative star products are the relative (for every Lie algebras) Kontsevich star products. 相似文献
8.
Ch. Ohn 《Letters in Mathematical Physics》1992,25(2):85-88
We obtain Zakrzewski's deformation of Fun SL(2) through the construction of a *-product on SL(2). We then give the deformation of
dual to this, as well as a Poincaré basis for both algebras.Aspirant au Fonds National belge de la Recherche Scientifique. Partially supported by EEC contract SC1-0105-C. 相似文献
9.
We consider SU
q
(2) covariant
-matrices for the reducible3 1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known
-matrices for SO
q
(3) and SO
q
(3, 1). Also, they are the three
-matrices which can be constructed by using four different SU
q
(2) doublets. Only two of the three
-matrices allow a differential structure on the reducible four-dimensional quantum space. 相似文献
10.
Pavel Šťovíček 《Czechoslovak Journal of Physics》2000,50(11):1353-1358
We discuss a modification ofU
q
and a class of its irreducible representations whenq is a root of unity.
Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. 相似文献
11.
BRST resolution is studied for the principally graded Wakimoto module of
recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. 相似文献
12.
Given a simple, simply laced, complex Lie algebra
corresponding to the Lie group G, let
be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra
whose underlying graded commutative algebra is given by the cohomology, with respect to
, of the algebra of regular functions on G with values in
. We conjecture that
describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical
string. The conjecture is verified in the two explicitly known cases,
2 (the Virasoro string) and
3 (the
string). 相似文献
13.
We develop a technique for the construction of integrable models with a 2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang–Baxter equations are written down and their solution for the gl(N) case is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group
, with a matrix deformation parameter q
such that (q
)2 = q
2. The symmetry behind these models can also be interpreted as the tensor product of the (–1)-Weyl algebra by an extension of
q
(gl(N)) with a Cartan generator related to deformation parameter –1. 相似文献
14.
We propose a q-deformation of the
-invariant Schrödinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but also to calculate the expectation values of some physically-relevant operators. Here we consider the case of the isotropic harmonic oscillator and of the quadrupole operator governing its interaction with an external field. We obtain the spectrum and wave functions both for
and generic
, and study the effects of the q-value range and of the arbitrariness in the
Casimir operator choice. We then show that the quadrupole operator in l=0 states provides a good measure of the deformation influence on the wave functions and on the Hilbert space spanned by them. 相似文献
15.
J. C. Hurtubise 《Letters in Mathematical Physics》1994,30(2):99-104
We give a classification of the finite dimensional coadjoint orbits in the dual of the algebra
+ of polynomials in one variable with values in a semi-simple Lie algebra
, and generalise this result to algebras defined over an arbitrary Riemann surface.During the preparation of this work the author was supported by NSERC grant A8361 and FCAR grant EQ3518. 相似文献
16.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
17.
José M. Figueroa-O'Farrill 《Communications in Mathematical Physics》1996,177(1):129-156
Let
be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if
is self-dual (that is, if it possesses an invariant metric) then it admits anN=1 (affine) Sugawara construction. Under certain additional hypotheses, thisN=1 structure admits anN=2 extension. If this is the case,
is said to possess anN=2 structure. It is also known that anN=2 structure on a self-dual Lie algebra
is equivalent to a vector space decomposition
, where
are isotropic Lie subalgebras. In other words,N=2 structures on
in one-to-one correspondence with Manin triples
. In this paper we exploit this correspondence to obtain a classification of thec=9N=2 structures on solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures. 相似文献
18.
For the gauge fields with values in arbitrary semisimple Lie algebra
we introduce the ansatzes which reduce the self-duality equations in the Euclidean spaceR
4,0 to the well-known Nahm equations. 相似文献
19.
We prove a simple formula for the transverse Poisson structure to a coadjoint orbit (in the dual of a Lie algebra
) and use it in examples such as
and
. We also give a sufficient condition on the isotropy subalgebra of
so that the transverse Poisson structureto the coadjoint orbit of is linear. 相似文献
20.
It was shown in an earlier paper that there is an Abelian extension
of the general linear algebra gl
2, that contains the current algebra with anomaly in 3+1 dimensions. We construct a three-parameter family of deformations
of
. For certain choices of the deformation parameters, we can construct unitary representations. We also construct highest-weight nonunitary representations for all choices of the parameters.This work was supported in part by U.S. Department of Energy Contract No. DE-AC02-76ER13065. 相似文献