2,675 research outputs found

### Minimal Affinizations of Representations of Quantum Groups: the simply--laced case

We continue our study of minimal affinizations for algebras of type D, E.Comment: 25 page

### Extended T-systems

We use the theory of q-characters to establish a number of short exact
sequences in the category of finite-dimensional representations of the quantum
affine groups of types A and B. That allows us to introduce a set of 3-term
recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic

### 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

### 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

### On the Correspondence between Poincar\'e Symmetry of Commutative QFT and Twisted Poincar\'e Symmetry of Noncommutative QFT

The space-time symmetry of noncommutative quantum field theories with a
deformed quantization is described by the twisted Poincar\'e algebra, while
that of standard commutative quantum field theories is described by the
Poincar\'e algebra. Based on the equivalence of the deformed theory with a
commutative field theory, the correspondence between the twisted Poincar\'e
symmetry of the deformed theory and the Poincar\'e symmetry of a commutative
theory is established. As a by-product, we obtain the conserved charge
associated with the twisted Poincar\'e transformation to make the twisted
Poincar\'e symmetry evident in the deformed theory. Our result implies that the
equivalence between the commutative theory and the deformed theory holds in a
deeper level, i.e., it holds not only in correlation functions but also in
(different types of) symmetries.Comment: 13 pages, minor corrections, version to appear in Phys. Rev.

### Minimal affinizations as projective objects

We prove that the specialization to q=1 of a Kirillov-Reshetikhin module for
an untwisted quantum affine algebra of classical type is projective in a
suitable category. This yields a uniform character formula for the
Kirillov-Reshetikhin modules. We conjecture that these results holds for
specializations of minimal affinization with some restriction on the
corresponding highest weight. We discuss the connection with the conjecture of
Nakai and Nakanishi on q-characters of minimal affinizations. We establish this
conjecture in some special cases. This also leads us to conjecture an
alternating sum formula for Jacobi-Trudi determinants.Comment: 25 page

### Many-spinon states and the secret significance of Young tableaux

We establish a one-to-one correspondence between the Young tableaux
classifying the total spin representations of N spins and the exact eigenstates
of the the Haldane-Shastry model for a chain with N sites classified by the
total spins and the fractionally spaced single-particle momenta of the spinons.Comment: 4 pages, 3 figure

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