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Related papers: Signature Characters for A_2 and B_2

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We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…

Representation Theory · Mathematics 2007-05-23 Vyjayanthi Chari , Adriano Moura

Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…

High Energy Physics - Theory · Physics 2009-10-22 T. Tjin

We decompose the tensor product of two irreducible representations of $\mathrm{GL}_2(\mathbb{F}_q)$ for odd $q$ and classify the pairs such that their tensor product is multiplicity free. We also classify the pairs such that their tensor…

Representation Theory · Mathematics 2023-10-25 Archita Gupta , M Hassain

We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for D between 3 and 7. The level decomposition with respect to the U-duality Lie algebra gives…

High Energy Physics - Theory · Physics 2014-02-18 Jakob Palmkvist

We show that the rigid C*-tensor categories of finite dimensional type 1 unitary representations of the quantum groups $U_{q}(\mathfrak{g}_{2})$ corresponding to the exceptional Lie group $G_2$ for positive $q\ne 1$ have property (T).

Operator Algebras · Mathematics 2015-11-05 Corey Jones

We study finite-dimensional representations of quantum affine algebras using q-characters. We prove the conjectures from math.QA/9810055 and derive some of their corollaries. In particular, we prove that the tensor product of fundamental…

Quantum Algebra · Mathematics 2009-10-31 Edward Frenkel , Evgeny Mukhin

We show that there are precisely two, up to conjugation, anti-involutions sigma_{\pm} of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight…

Quantum Algebra · Mathematics 2007-05-23 Victor G. Kac , Weiqiang Wang , Catherine H. Yan

We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any…

Rings and Algebras · Mathematics 2007-05-23 Alexander Premet , Helmut Strade

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

Quantum Algebra · Mathematics 2012-01-04 Dijana Jakelic , Adriano Moura

We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in…

Quantum Algebra · Mathematics 2025-01-29 Henrik Juergens

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime…

Representation Theory · Mathematics 2007-05-23 C. S. Rajan

We introduce and begin to study Lie theoretical analogs of symplectic reflection algebras for a finite cyclic group, which we call "cyclic double affine Lie algebra". We focus on type A : in the finite (resp. affine, double affine) case, we…

Representation Theory · Mathematics 2009-11-05 Nicolas Guay , David Hernandez , Sergey Loktev

We prove that among the finite dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the property that the middle term of an arbitrary extension of indecomposable modules has at…

Representation Theory · Mathematics 2021-05-10 Mariano Suárez-Álvarez

We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form…

Quantum Algebra · Mathematics 2025-06-23 Stephen T. Moore

In this article we calculate the signature character of certain Hermitian representations of $GL_N(F)$ for a $p$-adic field $F$. We further give a conjectural description for the signature character of unramified representations in terms of…

Representation Theory · Mathematics 2011-02-19 C. Boyallian , T. Wedhorn

Given a parametrised weight function $\omega(x,\mu)$ such that the quotients of its consecutive moments are M\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \cite{IN2}. In the present paper…

Classical Analysis and ODEs · Mathematics 2015-06-26 Arieh Iserles , Syvert Paul Nørsett

We give an explicit isomorphism between the Gassner representation and the first weight level of a representation of quantum sl(2). Then we construct and provide matrices for colored versions of the BKL representation and higher Lawrence's…

Geometric Topology · Mathematics 2020-04-10 Jules Martel

We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories…

Representation Theory · Mathematics 2026-03-03 Shun-Jen Cheng , Weiqiang Wang

We construct a class of negative spin irreducible representations of the su(2) Lie algebra. These representations are infinite-dimensional and have an indefinite inner product. We analyze the decomposition of arbitrary products of positive…

High Energy Physics - Theory · Physics 2007-05-23 Andre van Tonder

We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld "coproduct". This allow us to recover the vector representations recently introduced by Feigin-Jimbo-Miwa-Mukhin [6] and…

Quantum Algebra · Mathematics 2015-01-26 Mathieu Mansuy
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