共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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
3.
Lucy Gow 《Czechoslovak Journal of Physics》2005,55(11):1415-1420
Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y
of the general linear Lie algebra
. In this article, we extend some of their ideas to consider the Yangian Y
of the Lie superalgebra
. In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
4.
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
5.
We establish an explicit isomorphism between two realizations of the quantum affine algebra
given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra
. 相似文献
6.
We study analogues of the Yangian of the Lie algebra
for the other classical Lie algebras
and
. We call them twisted Yangians. They are coideal subalgebras in the Yangian of
and admit homomorphisms onto the universal enveloping algebras U(
) and U(
) respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in U(
) and U(
) of these subalgebras are also maximal commutative. 相似文献
7.
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
8.
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
9.
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
10.
Hitoshi Konno 《Czechoslovak Journal of Physics》2005,55(11):1455-1460
We give a level-2 representation of the elliptic algebra
in terms of one free boson and one free fermion. We show that
-modules have a natural direct sum decomposition into the irreducible (deformed) super-Virasoro modules associated with the
coset
.
Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005. 相似文献
11.
D. Arnaudon 《Czechoslovak Journal of Physics》1997,47(11):1075-1082
Irreducible representations of
at roots of unity in the restricted specialisation are described with the Gelfand-Zetlin basis. This basis is redefined to allow the Casimir operator of the quantum subalgebra
not to be completely diagonalised. Some irreducible representations of
indeed contain indecomposable
-modules. The set of redefined (mixed) states is described as a teepee inside the pyramid made with the whole representation. 相似文献
12.
Sergio Doplicher Daniel Kastler Derek W. Robinson 《Communications in Mathematical Physics》1966,3(1):1-28
Starting from aC*-algebra
and a locally compact groupT of automorphisms of
we construct a covariance algebra
with the property that the corresponding *-representations are in one-to-one correspondence with covariant representations of
i.e. *-representations of
in which the automorphisms are continuously unitarily implemented. We further construct for relativistic field theory an algebra
yielding the *-representations of
in which the space time translations have their spectrum contained inV. The problem of denumerable occurence of superselection sectors is formulated as a condition on the spectrum of
. Finally we consider the covariance algebra
built with space translations alone and show its relevance for the discussion of equilibrium states in statistical mechanics, namely we restore in this framework the equivalence of uniqueness of the vacuum, irreducibility and a weak clustering property.On leave of absence from Istituto di Fisica G. Marconi — Roma. 相似文献
13.
B. Enriquez 《Communications in Mathematical Physics》1995,170(1):197-206
We propose a quantum lattice version of B. Feigin and E. Frenkel's constructions, identifying the KdV differential polynomials with functions on a homogeneous space under the nilpotent part of
. We construct an action of the nilpotent part
of
on their lattice counterparts, and embed the lattice variables in a
, coinduced from a quantum version of the principal commutative subalgebra, which is defined using the identification of
with its dual algebra. 相似文献
14.
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
15.
Hirokazu Nishimura 《International Journal of Theoretical Physics》1994,33(6):1173-1188
Any manual
of Boolean locales in the strong sense, namely a subcategory of the opposite category
of the category
of complete Boolean algebras and complete Boolean homomorphisms satisfying not only conditions (3.1)–(3.10) of our previous paper [International Journal of Theoretical Physics,32, 1293 (1993b)], but also conditions (4.1)–(4.4) of that paper, is shown to be representable as the second-class orthomodular manual
of Boolean locales on an orthomodular poset
In this sense the study on manuals of Boolean locales in the strong sense is tantamount to the study on a special class of orthomodular posets, though our viewpoint is radically different from the conventional one in the traditional approach to orthomodular posets. Then the notion of a manual of Hilbert spaces or exactly what is called a manual of Hilbert locales is introduced, over which a variant of the celebrated Gelfand-Naimark-Segal theorem for a manual of Boolean locales in the strong sense is established. 相似文献
16.
Theq=0 combinatorics for
is studied in connection with solvable lattice models. Crystal bases of highest weight representations of
are labelled by paths which were introduced as labels of corner transfer matrix eigenvectors atq=0. It is shown that the crystal graphs for finite tensor products ofl-th symmetric tensor representations of
approximate the crystal graphs of levell representations of
. The identification is made between restricted paths for the RSOS models and highest weight vectors in the crystal graphs of tensor modules for
.Partially supported by NSF grant MDA904-90-H-4039 相似文献
17.
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
18.
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
19.
Representations of theC*-algebra
of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of
onto its commutant. This means that there is an equivalent anti-linear representation of
in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed. 相似文献
20.
The theorem that each derivation of aC*-algebra
extends to an inner derivation of the weak-operator closure (
)– of
in each faithful representation of
is proved in sketch and used to study the automorphism group of
in its norm topology. It is proved that the connected component of the identity in this group contains the open ball of radius 2 with centerl and that each automorphism in extends to an inner automorphism of (
)–.Research conducted with the partial support of the NSF and ONR. 相似文献