Related papers: Extension Quiver for Lie Superalgebra $\mathfrak{q…

We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle…

We construct a special principal series representation for the modular double $U_{q\tilde{q}}(g_R)$ of type $A_r$ representing the generators by positive essentially self-adjoint operators satisfying the transcendental relations that also…

We calculate the blocks of the category of finite-dimensional representations of W(0,n), with n > 2, and show that all are of wild type. As an application, we show that the centre of the universal enveloping algebra is trivial.

We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique…

We provide an explicit combinatorial realization of all simple and injective (hence, and projective) modules in the category of bounded $\mathfrak{sp}(2n)$-modules. This realization is defined via a natural tableaux correspondence between…

Let $\mathfrak{g}$ be a complex simple Lie algebra and $U_q(\hat{\mathfrak{g}})$ the corresponding quantum affine algebra. We prove that every irreducible finite-dimensional $U_q(\hat{\mathfrak{g}})$-module gives rise to a family of…

The q-field theories are constructed by substituting quantum groups for the usual Lie groups. In earlier papers this construction was carried out for the quantum group SU_q(2). Here the investigation is extended to SL_q(3). The resulting…

We explore the (noncommutative) geometry of locally simple representations of the diagonal locally finite Lie algebras $\mathfrak{sl}(n^\infty)$, $\mathfrak o(n^\infty)$, and $\mathfrak{sp}(n^\infty)$. Let $\mathfrak g_\infty$ be one of…

Starting from a collection of line bundles on a projective toric orbifold X, we introduce a stacky analogue of the classical linear series. Our first main result extends work of King by building moduli stacks of refined representations of…

Let Q be a connected directed quiver with n vertices. We show that Q is representation-infinite if and only if there do exist n isomorphism classes of exceptional modules of some fixed length at least 2.

In this paper we continue the study of representation theory of formal distribution Lie superalgebras initiated in q-alg/9706030. We study finite Verma-type conformal modules over the N=2, N=3 and the two N=4 superconformal algebras and…

We study the Ext-algebra of the direct sum of all parabolic Verma modules in the principal block of the Bernstein-Gelfand-Gelfand category O for the hermitian symmetric pair $(\mathfrak{gl}_{n+m}, \mathfrak{gl}_{n} \oplus \mathfrak{gl}_m)$…

We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove existence of uniform expander representations for any wild quiver…

We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules.…

In this paper, we study the relationship between the McKay quivers of a finite subgroups $G$ of special linear groups general linear groups, via some natural extension and embedding. We show that the McKay quiver of certain extension of a…

For each simple Lie algebra $\mathfrak{g}$, we construct an algebra embedding of the quantum group $U_q(\mathfrak{g})$ into certain quantum torus algebra $D_\mathfrak{g}$ via the positive representations of split real quantum group. The…

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…

Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group $SU_q(2)$ as a fibre. Both hierarchies are…

We determine the Grothendieck rings of the category of finite-dimensional modules over Queer Lie superalgebras via their rings of characters. In particular, we show that the ring of characters of the Queer Lie supergroup $Q(n)$ is…

We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the decomposition matrix of a finite group with split BN-pair, with respect to a…