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

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…

Let $C$ be a symmetrizable generalized Cartan Matrix, and $q$ an indeterminate. ${\fg}(C)$ is the Kac-Moody Lie algebra and $U=U_q({\fg}(C))$ the associated quantum enveloping algebra over $ k={\Bbb Q}(q)$. The quantum function algebra…

We define the categories of weight-finite modules over the type $\mathfrak a_1$ quantum affine algebra $\dot{\mathrm{U}}_q(\mathfrak a_1)$ and over the type $\mathfrak a_1$ double quantum affine algebra $\ddot{\mathrm{U}}_q(\mathfrak a_1)$…

We define and study the space of $q$-opers associated with Bethe equations for integrable models of XXZ type with quantum toroidal algebra symmetry. Our construction is suggested by the study of the enumerative geometry of cyclic quiver…

Let $W$ be a finite Weyl group of classical type which may not be irreducible, $F$ an algebraically closed field, $q$ an invertible element of $F$. We denote by $\mathcal H_W(q)$ the associated Hecke algebra. If $q=1$ then it is $FW$ and we…

We classify unitary highest weight modules with a given integral infinitesimal character for the real Lie algebras $\mathfrak{su}(p,q)$ and $\mathfrak{so}^*(2n)$. We treat both regular and singular cases. For $\mathfrak{su}(p,q)$ we…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

We establish the method of Bethe ansatz for the XXZ type model obtained from the R-matrix associated to quantum toroidal gl(1). We do that by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is…

For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p.…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

Let $k$ be a field and let $E$ be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra $L_k (E)$ and show its close relationship with the finite-dimensional representations…

Let $\g$ be a reductive Lie algebra and $V$ a $\g$-semisimple module. In this article, we study the category $\G$ of graded finite-dimensional representations of $\g \ltimes V$. We produce a large class of truncated subcategories, which are…

Let E be a finite extension of Fp. Using Fontaine's theory of (phi,Gamma)-modules, Colmez has shown how to attach to any irreducible E-linear representation of Gal(Qpbar/Qp) an infinite dimensional smooth irreducible E-linear representation…

Let $G$ be a finite group such that $\text{SL}(n,q)\subseteq G \subseteq \text{GL}(n,q)$ and $Z$ be a central subgroup of $G$. In this paper we determine the group $T(G/Z)$ consisting of the equivalence classes of endotrivial…

It is proved that an irreducible quasifinite $W_\infty$-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight $W_\infty$-module is a module of the intermediate series.…

This work provides the first step toward the classification of irreducible finite weight modules over twisted affine Lie superalgebras. We study all such modules whether the canonical central element acts as a nonzero multiple of the…

In this work we construct an eigencurve for p-adic modular forms attached to an indefinite quaternion algebra over Q. Our theory includes the definition, both as rules on test objects and sections of line bundle, of p-adic modular forms,…

Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field $k$, $T_2(A)=(\begin{array}{cc}A&0 A&A\end{array})$ be the triangular matrix algebra and $A^{(1)}=(\begin{array}{cc}A&0 DA&A\end{array})$ be the…

We study the properties of level zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by Akasaka and the present author is given. Several properties of modules generated by extremal…