Related papers: Virtual representation motives

We propose a matrix regularization of vector bundles over a general closed K\"ahler manifold. This matrix regularization is given as a natural generalization of the Berezin-Toeplitz quantization and gives a map from sections of a vector…

We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to be related to branes in the moduli space of G-Higgs bundles…

The Attractor Conjecture for Calabi-Yau moduli spaces predicts the algebraicity of the moduli values of certain isolated points picked out by Hodge-theoretic conditions. We provide a family of counterexamples to the Attractor Conjecture in…

A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…

A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of $G$-zips of connected-Hodge-type; such schemes should include all…

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 X be as smooth complex projective variety with Neron-Severi group isomorphic to Z, and D an irreducible divisor with normal crossing singularities. Assume r is equal to 2 or 3. We prove that if the fundamental group of X doesn't have…

We study the representation theory of the rook-Brauer algebra RB_k(x), also called the partial Brauer algebra. This algebra has a basis of "rook-Brauer" diagrams, which are Brauer diagrams that allow for the possibility of missing edges.…

We introduce local invariants of algebraic spaces and stacks which measure how far they are from being a scheme. Using these invariants, we develop mostly topological criteria to determine when the moduli space of a stack is a scheme. As an…

A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomology theory A(-) with a special linear orientation and…

For a smooth projective surface $X$ satisfying $H_1(X,\mathbb{Z}) = 0$ and $w \in H^2(X,\mu_r)$, we study deformation invariants of the pair $(X,w)$. Choosing a Brauer-Severi variety $Y$ (or, equivalently, Azumaya algebra $\mathcal{A}$)…

In 1980 Zelevinsky introduced commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate…

The quantum general linear supergroup GLq(m|n) is defined and its structure is studied systematically. Quantum homogeneous supervector bundles are introduced following Connes' theory, and applied to develop the representation theory of…

It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…

Let $H$ be a subgroup of ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) such that the Zariski closure in ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) of some compact subgroup of $H$ contains $H$. We…

Let V_0 and V_1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V_0 and V_1 can be embedded in a bundle U in such a way that V_0\cap…

We construct smooth rational real algebraic varieties of every dimension $\ge$ 4 which admit infinitely many pairwise non-isomorphic real forms.

Given any irreducible smooth complex projective curve $X$, of genus at least $2$, consider the moduli stack of vector bundles on $X$ of fixed rank and determinant. It is proved that the isomorphism class of the stack uniquely determines the…

Over the past three decades, it has been shown that discrete and continuous media can support topologically nontrivial waves. Recently, it was shown that the same is true of the vacuum, in particular, right (R) and left (L) circularly…

In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic…