Related papers: Vector bundles on quantum conjugacy classes

Let $\mathcal{O}^{int}_q(m|n)$ be a semisimple tensor category of modules over a quantum ortho-symplectic superalgebra of type $B, C, D$ introduced in the author's previous work. It is a natural counterpart of the category of finitely…

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…

We describe the components of the moduli space of conjugacy classes of commuting pairs and triples of elements in a compact Lie group. This description is in terms of the extended Dynkin diagram of the simply connected cover, together with…

Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple…

Let $\mathfrak{g}$ be a symmetrizable Kac--Moody algebra. We describe {standard graded} $\mathfrak{g}$-modules $V$, which we use to construct a completion $\widehat{V}$ and pro-unipotent group $\widehat{U}$ in $\GL(\widehat{V})$. These…

Let G be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k fusion ring R_k(G) of G with the twisted equivariant K-homology at level k+h, where h is the dual Coxeter number. In this…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham…

We generalize the higher Riemann-Hilbert correspondence in the presence of scalar curvature for a (possibly non-compact) smooth manifold $M$. We show that the dg-category of curved $\infty$-local systems, the dg-category of graded vector…

Let $Y$ be a scheme in which 2 is invertible and let $V$ be a rank $n$ vector bundle on $Y$ endowed with a non-degenerate symmetric bilinear form $q$. The orthogonal group ${\bf O}(q)$ of the form $q$ is a group scheme over $Y$ whose…

This paper is devoted to the representation theory of quantum coordinate algebra $\mathbb{C}_q[G]$, for a semisimple Lie group $G$ and a generic parameter $q$. By inspecting the actions of normal elements on tensor modules, we generalize a…

In previous work, the second author and others have found conditions on a homogeneous space $G/H$ which imply that, up to stabilization, all vector bundles over $G/H$ admit Riemannian metrics of non-negative sectional curvature. One…

Let $G$ be a complex semisimple Lie group and $\mathfrak g$ its Lie algebra. In this paper, we study a special class of cyclic Higgs bundles constructed from a $\mathbb Z$-grading $\mathfrak g = \bigoplus_{j=1-m}^{m-1}\mathfrak g_j$ by…

Let $\mathbb{K}$ be a number field with ring of integers $\mathfrak{O}$ and let $\mathcal{G}$ be a Chevalley group scheme not of type $\mathtt{E}_8$, $\mathtt{F}_4$ or $\mathtt{G}_2$. We use the theory of Tits buildings and a result of…

Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(kQ), is equivalent to several other categories: the…

In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…

We formulate a notion of jet bundles over a possibly noncommutative algebra $A$ equipped with a torsion free connection. Among the conditions needed for 3rd-order jets and above is that the connection also be flat and its `generalised…

This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(\mathfrak{g})$, Yangian $Y(\mathfrak{g})$ and…

We provide an explicit quantization of dynamical r-matrices for semisimple Lie algebras, classified earlier by the third author, which includes the Belavin-Drinfeld r-matrices. We do so by constructing an appropriate (dynamical) twist in…