On multigraded generalizations of Kirillov-Reshetikhin modules

We study the category of Z^l-graded modules with finite-dimensional graded pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre subcategories with finitely many isomorphism classes of simple objects. We construct projective resolutions for the simple modules in these categories and compute the Ext groups between simple modules. We show that the projective covers of the simple modules in these Serre subcategories can be regarded as multigraded generalizations of Kirillov-Reshetikhin modules and give a recursive formula for computing their graded characters

Non-Commutative Geometry and Twisted Conformal Symmetry

The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the Poincar\'e algebra and the construction is then extended to the full conformal algebra. It is demonstrated that conformal invariance need not be viewed as incompatible with non-commutative geometry; the non-commutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincar\'e algebra.Comment: 8 pages; REVTeX; V2: Reference adde

Equivariant map superalgebras

Suppose a group $\Gamma$ acts on a scheme $X$ and a Lie superalgebra $\mathfrak{g}$. The corresponding equivariant map superalgebra is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. We classify the irreducible finite dimensional modules for these superalgebras under the assumptions that the coordinate ring of $X$ is finitely generated, $\Gamma$ is finite abelian and acts freely on the rational points of $X$, and $\mathfrak{g}$ is a basic classical Lie superalgebra (or $\mathfrak{sl}(n,n)$, $n > 0$, if $\Gamma$ is trivial). We show that they are all (tensor products of) generalized evaluation modules and are parameterized by a certain set of equivariant finitely supported maps defined on $X$. Furthermore, in the case that the even part of $\mathfrak{g}$ is semisimple, we show that all such modules are in fact (tensor products of) evaluation modules. On the other hand, if the even part of $\mathfrak{g}$ is not semisimple (more generally, if $\mathfrak{g}$ is of type I), we introduce a natural generalization of Kac modules and show that all irreducible finite dimensional modules are quotients of these. As a special case, our results give the first classification of the irreducible finite dimensional modules for twisted loop superalgebras.Comment: 27 pages. v2: Section numbering changed to match published version. Other minor corrections. v3: Minor corrections (see change log at end of introduction

Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

N-enlarged Galilei Hopf algebra and its twist deformations

The N-enlarged Galilei Hopf algebra is constructed. Its twist deformations are considered and the corresponding twisted space-times are derived.Comment: 8 pages, no figure

On minimal affinizations of representations of quantum groups

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of Nakai-Nakanishi (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physic

Enhancing the Benefits for India and Other Developing Countries in the Doha Development Agenda Negotiations

When firms from developed markets acquire firms in emerging markets, marketcapitalization-weighted monthly joint returns show a statistically significant increase of 1.8%. Panel data estimations suggest that the value gains from cross-border M&A transactions stem from the transfer of majority control from emerging-market targets to developed market acquirers—joint returns range from 5.8% to 7.8% when majority control is acquired. Announcement returns for acquirer and target firms estimate the distribution of gains and show a statistically significant increase of 2.4% and 6.9%, respectively. The evidence suggests that the stock market anticipates significant value creation from cross-border transactions that involve emerging-market targets leading to substantial gains for shareholders of both acquirer and target firms.

Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

Let Uq(ghat) be the quantum affine algebra associated to a simply-laced simple Lie algebra g. We examine the relationship between Dorey's rule, which is a geometrical statement about Coxeter orbits of g-weights, and the structure of q-characters of fundamental representations V_{i,a} of Uq(ghat). In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and sufficient condition for the monomial 1 to appear in the q-character of a three-fold tensor product V_{i,a} x V_{j,b} x V_{k,c}.Comment: 30 pages, latex; v2, to appear in Communications in Mathematical Physic

Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent

The Moyal and Wick-Voros planes A^{M,V}_{\theta} are *-isomorphic. On each of these planes the Poincar\'e group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors. We show that the *-isomorphism T: A^M_{\theta} to A^V_{\theta} does not also map the corresponding twists of the Poincar\'e group algebra. The quantum field theories on these planes with twisted Poincar\'e-Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a non-trivial dependence on the non-commutative parameter is present for the Wick-Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields). Our results differ from these of (arXiv:0810.2095 [hep-th]) because of differences in the treatments of quantum field theories.Comment: 12 page

SO(5) structure of p-wave superconductivity for spin-dipole interaction model

A closed SO(5) algebraic structure in the the mean-field form of the Hamiltonian the pure p-wave superconductivity is found that can help to diagonalized by making use of the Bogoliubov rotation instead of the Balian-Werthamer approach. we point out that the eigenstate is nothing but SO(5)-coherent state with fermionic realization. By applying the approach to the Hamiltonian with dipole interaction of Leggett the consistency between the diagonalization and gap equation is proved through the double-time Green function. The relationship between the s-wave and p-wave superconductivities turns out to be recognized through Yangian algebra, a new type of infinite-dimensional algebra.Comment: 7 pages, no figures. Accepted Journal of Physcis A: Mathematical and Genera