相关论文: Factorizable ribbon quantum groups in logarithmic …

The present paper continues the work of [10] and [6]. For any symmetrizable generalized Cartan Matrix $C$ and the corresponding quantum group $\mathbf{U}$, we consider the associated quiver $Q$ with an admissible automorphism $a$. We…

The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular,…

Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure…

We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…

In some recent work, Lusztig outlined a generalisation of the construction of Deligne and Lusztig to reductive groups over finite rings coming from the ring of integers in a local field, modulo some power of the maximal ideal. Lusztig…

We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…

We establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent super Cartan datum by constructing an automorphism (called twistor) in the setting of covering quantum groups. The…

We prove a formula for the dimension of Whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups. The formula explicitly relates such dimension to the Kazhdan-Lusztig…

We show that Lusztig's theories of two-sided cells and non-unipotent representations of a reductive group over a finite field are compatible with the V. Lafforgue's automorphic-to-galois direction of the Langlands correspondence. To do…

The groups of (linear) similarity and coincidence isometries of certain modules in d-dimensional Euclidean space, which naturally occur in quasicrystallography, are considered. It is shown that the structure of the factor group of…

We find a quantum group structure in two-dimensional motion of nonrelativistic electrons in a uniform magnetic field on a torus. The representation basis of the quantum algebra is composed of the quantum Hall wavefunctions proposed by…

We prove the Berenstein-Zelevinsky conjecture that the quantized coordinate rings of the double Bruhat cells of all finite dimensional simple algebraic groups admit quantum cluster algebra structures with initial seeds as specified by [4].…

We study the dual constructions of quantum loop groups and Feigin-Odesskii type shuffle algebras for an arbitrary quiver, for which the arrow parameters are arbitrary non-zero elements of any field. Examples of our setup include…

Graded Hecke algebras can be constructed in terms of equivariant cohomology and constructible sheaves on nilpotent cones. In earlier work, their standard modules and their irreducible modules where realized with such geometric methods. We…

This thesis contains results relevant for two different classes of conformal field theory. We partly treat rational conformal field theory, but also derive results that aim at a better understanding of logarithmic conformal field theory.…

Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over…

The integral group rings $\mathbb{Z}G$ for finite groups $G$ are precisely those fusion rings whose basis elements have Frobenius-Perron dimension 1, and each is categorifiable in the sense that it arises as the Grothendieck ring of a…

We introduce a family of factorisable ribbon quasi-Hopf algebras $Q(N)$ for $N$ a positive integer: as an algebra, $Q(N)$ is the semidirect product of $\mathbb{C}\mathbb{Z}_2$ with the direct sum of a Grassmann and a Clifford algebra in…

We discuss the proof of Kazhdan and Lusztig of the equivalence of the Drinfeld category D(g,h) of g-modules and the category of finite dimensional Uq(g)-modules, q=exp(\pi ih), for h\in C\Q*. Aiming at operator algebraists the result is…

Twisted modules over vertex algebras formalize the relations among twisted vertex operators and have applications to conformal field theory and representation theory. A recent generalization, called twisted logarithmic module, involves the…