共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
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
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.
Lucy Gow 《Communications in Mathematical Physics》2007,276(3):799-825
We describe a Gauss decomposition for the Yangian of the general linear Lie superalgebra. This gives a connection between this Yangian and the Yangian of the classical Lie
superalgebra Y(A(m − 1, n − 1)) (for m ≠ n) defined and studied in papers by Stukopin, and suggests natural definitions for the Yangians and Y(A(n, n)). We also show that the coefficients of the quantum Berezinian generate the centre of the Yangian . This was conjectured by Nazarov in 1991. 相似文献
6.
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
7.
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
8.
We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category for the queer Lie superalgebra are equivalent to the corresponding blocks of the category for the Lie algebra . 相似文献
9.
S. Lievens N. I. Stoilov J. Van der Jeugt 《Communications in Mathematical Physics》2008,281(3):805-826
It is known that the defining relations of the orthosymplectic Lie superalgebra are equivalent to the defining (triple) relations of n pairs of paraboson operators . In particular, with the usual star conditions, this implies that the “parabosons of order p” correspond to a unitary irreducible (infinite-dimensional) lowest weight representation V(p) of . Apart from the simple cases p = 1 or n = 1, these representations had never been constructed due to computational difficulties, despite their importance. In the
present paper we give an explicit and elegant construction of these representations V(p), and we present explicit actions or matrix elements of the generators. The orthogonal basis vectors of V(p) are written in terms of Gelfand-Zetlin patterns, where the subalgebra of plays a crucial role. Our results also lead to character formulas for these infinite-dimensional representations. Furthermore, by considering the branching , we find explicit infinite-dimensional unitary irreducible lowest weight representations of and their characters.
NIS was supported by a project from the Fund for Scientific Research – Flanders (Belgium) and by project P6/02 of the Interuniversity
Attraction Poles Programme (Belgian State – Belgian Science Policy).
An erratum to this article can be found at 相似文献
10.
P. Zinn-Justin 《Communications in Mathematical Physics》2007,272(3):661-682
Integrable loop models associated with higher representations (spin ℓ/2) of are investigated at the point . The ground state eigenvalue and eigenvectors are described. Introducing inhomogeneities into the models allows to derive
a sum rule for the ground state entries.
Supported by ANR program “GIMP” ANR-05-BLAN-0029-01, European networks “ENIGMA” MRT-CT-2004-5652, “ENRAGE” MRTN-CT-2004-005616,
and ESF program “MISGAM”. 相似文献
11.
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
12.
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
13.
Generalizing the $$\mathfrak {bms}_{3}$$ and 2D-conformal algebras by expanding the Virasoro algebra
Ricardo Caroca Patrick Concha Evelyn Rodríguez Patricio Salgado-Rebolledo 《The European Physical Journal C - Particles and Fields》2018,78(3):262
By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the \(\mathfrak {bms}_{3}\) algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called \(\mathfrak {B}_{k}\), \(\mathfrak {C}_{k}\) and \(\mathfrak {D}_{k}\) algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Ka?–Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed. 相似文献
14.
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
15.
We compute the first cohomology spaces
of the Lie superalgebra with coefficients in the superspace of linear differential operators acting on weighted densities on the supercircle S
1|1. The structure of these spaces was conjectured in (Gargoubi et al. in Lett Math Phys 79:5165, 2007). In fact, we prove here
that the situation is a little bit more complicated.
相似文献
16.
I. L. Buchbinder E. A. Ivanov O. Lechtenfeld I. B. Samsonov B. M. Zupnik 《Physics of Particles and Nuclei》2008,39(5):759-797
We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality
and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific
backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus
is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed
transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian
case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective
action.
The text was submitted by the authors in English. 相似文献
17.
18.
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
19.
20.
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