Related papers: Finite type modules and Bethe Ansatz for quantum t…

We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification…

Let $V$ be a highest weight module over a Kac-Moody algebra $\mathfrak{g}$, and let conv $V$ denote the convex hull of its weights. We determine the combinatorial isomorphism type of conv $V$, i.e. we completely classify the faces and their…

We construct a $(\mathfrak{gl}_2, B(\mathbb{Q}_p))$ and Hecke-equivariant cup product pairing between overconvergent modular forms and the local cohomology at $0$ of a sheaf on $\mathbb{P}^1$, landing in the compactly supported completed…

Let $G$ be a simple algebraic group of type $A$ or $D$ defined over $\C$ and $T$ be a maximal torus of $G$. For a dominant coweight $\lambda$ of $G$, the $T$-fixed point subscheme $(\bar{Gr}_G^\lambda)^T$ of the Schubert variety…

We extend Auslander and Buchsbaum's Euler characteristic from the category of finitely generated modules of finite projective dimension to the category of modules of finite G-dimension using Avramov and Martsinkovsky's notion of relative…

As is well known, the type 1 Lie superalgebra sl(r+1|s+1) admits a one parameter family of finite dimensional irreducible representations. We have carried out an analytic Bethe ansatz related to this family of representations. We present…

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

In this paper, we characterize quasi-integrable modules, of nonzero level, over twisted affine Lie superalgebras. We show that quasi-integrable modules are not necessarily highest weight modules. We prove that each quasi-integrable module…

In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo,…

Chari and Greenstein [Adv. Math. 2009] introduced combinatorial subsets of the roots of a finite-dimensional simple Lie algebra $\mathfrak{g}$ which were important in studying Kirillov-Reshetikhin modules over $U_q(\widehat{\mathfrak{g}})$…

Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and…

Following the work of Venkatesh (arXiv:2203.03158), we study further the categories of representations of the general linear groups $GL(X)$ in the Verlinde category $Ver_p$ in characteristic $p$. The main question we answer is how to…

We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…

Let $G={\rm SL}_2(\mathfrak F) $ where $\mathfrak F$ is a finite extension of $\mathbb Q_p$. We suppose that the pro-$p$ Iwahori subgroup $I$ of $G$ is a Poincar\'e group of dimension $d$. Let $k$ be a field containing the residue field of…

We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by $\pm 1$. We…

Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \…

We investigate the algebraic structure of a recently proposed integrable $t-J$ model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz…

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class…

We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian $Y(X_r)$ or its quantum affine analogue $U_q(X^{(1)}_r)$ for $X_r = B_r, C_r$ and $D_r$. Eigenvalue formulas are proposed for the transfer matrices…

We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We…