相关论文: Higher order Kirillov-Reshetikhin modules, Imagina…

Motivated by the limitations of cluster algebra techniques in detecting imaginary modules, we build on the representation-theoretic framework developed by the first author and Chari to extend the construction of such modules beyond…

In this survey, we shall be concerned with the category of finite-dimensional representations of the untwisted quantum affine algebras when the quantum parameter q is not a root of unity. We review the foundational results of the subject,…

We introduce a new family of real simple modules over the quantum affine algebras, called the affine determinantial modules, which contains the Kirillov-Reshetikhin (KR)-modules as a special subfamily, and then prove T-systems among them…

We show the denominator formulas for the normalized $R$-matrix involving two arbitrary Kirillov--Reshetikhin (KR) modules $W^{(k)}_{m,a}$ and $W^{(l)}_{p,b}$ in all nonexceptional affine types, $D_4^{(3)}$, and $G_2^{(1)}$. To achieve our…

A braided tensor category $FM_{\kappa}$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $FS_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite…

For a quantum affine algebra of type A, we describe the composition series of the tensor product of a general minimal affinization with a Kirillov-Resehtikhin module associated to an extreme node of the Dynkin diagram of the underlying…

We prove a uniqueness theorem for irreducible non-critical Gelfand-Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand-Tsetlin modules with 1-singularity. An explicit construction of such…

Let $\mathcal{D}$ be the Drinfeld double of $\mathcal{FK}_3\#\Bbbk{\mathbb S}_3$. The simple $\mathcal{D}$-modules were described in arXiv:1409.0438. In the present work, we describe the indecomposable summands of the tensor product between…

The concept of pseudo q-factorization graphs was recently introduced by the last two authors as a combinatorial language which is suited for capturing certain properties of Drinfeld polynomials. Using certain known representation theoretic…

The class of quantum affinizations includes quantum affine algebras and quantum toroidal algebras. In general they have no Hopf algebra structure, but have a "coproduct" (the Drinfeld coproduct) which does not produce tensor products of…

We introduce and study a category of representations of the Borel algebra, associated with a quantum loop algebra of non-twisted type. We construct fundamental representations for this category as a limit of the Kirillov-Reshetikhin modules…

We revisit the derivation of Knizhnik-Zamolodchikov equations in the case of nonsemisimple categories of modules of a superalgebra in the case of the generic affne level and representations parameters. A proof of existence of asymptotic…

We construct a higher level analogue of Dorey's rule, which describe certain surjective morphisms between Kirillov--Reshetikhin (KR) modules over quantum affine algebras. Building on this, we establish a generalized T-system of short exact…

This article is divided in two parts. In the first part we endow a certain ring of ``Drinfeld quasi-modular forms'' for $\GL_2(\FF_q[T])$ (where $q$ is a power of a prime) with a system of "divided derivatives" (or hyperderivations). This…

We continue the study of the Drinfeld double of the Jordan plane, denoted by $\mathcal D$ and introduced in arXiv:2002.02514. The simple finite-dimensional modules were computed in arXiv:2108.13849; it turns out that they factorize through…

We show that a $q$-character of a Kirillov-Reshetikhin module (KR modules) for untwisted quantum affine algebras of simply laced types $A_n^{(1)}$, $D_n^{(1)}$, $E_6^{(1)}$, $E_7^{(1)}$, $E_8^{(1)}$ might be obtained from a specific cluster…

Let $U_q'(\mathfrak{g})$ be a quantum affine algebra of untwisted affine $ADE$ type, and $\mathcal{C}_{\mathfrak{g}}^0$ the Hernandez-Leclerc category of finite-dimensional $U_q'(\mathfrak{g})$-modules. For a suitable infinite sequence…

We work with detail the Drinfeld module over the ring $$A=F_2[x,y]/(y^2+y=x^3+x+1).$$ The example in question is one of the four examples that come from quadratic imaginary fields with class number $h = 1$ and rank one. We develop specific…

For any acyclic quiver $Q$ without multiple edges, we construct a monoidal category $\mathcal{R}_Q$ whose indecomposable objects are tensor products (over the base field) of finite-dimensional modules over the path algebra of $Q$. We show…

We consider generalized Haagerup categories such that $1 \oplus X$ admits a $Q$-system for every non-invertible simple object $X$. We show that in such a category, the group of order two invertible objects has size at most four. We describe…