Related papers: The space of generalized G2-theta functions

In this paper we give a survey of various results about the topology of oriented Grassmannian bundles related to the exceptional Lie group G_2. Some of these results are new. We give self-contained proofs here. One often encounters these…

In this paper, generalized Cayley graphs are studied. It is proved that every generalized Cayley graph of order 2p is a Cayley graph, where p is a prime. Special attention is given to generalized Cayley graphs on Abelian groups. It is…

If C is a smooth projective curve over a number field k, then, under fair hypotheses, its L-function admits meromorphic continuation and satisfies the anticipated functional equation if and only if a related function is X-mean-periodic for…

In this paper we study the cohomology of (strict) Lie 2-groups. We obtain an explicit Bott-Shulman type map in the case of a Lie 2-group corresponding to the crossed module $A\to 1$. The cohomology of the Lie 2-groups corresponding to the…

Let $G = GL(V)$ for an N-dimensional vector space $V$ over an algebraically closed field k, and $G^{\theta}$ the fixed point subgroup of $G$ under an involution $\theta$ on $G$. In the case where $G^{\theta} = O(V)$, the generalized…

Let $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a connected nonsingular projective curve over $k$ with genus $g \geq 2$. This paper continues the work begun by Lehr and Matignon, namely the study of "big actions",…

Let G be a Lie group, $T^*G$ its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action…

We introduce a new class of $\mathfrak{sl}_2$-triples in a complex simple Lie algebra $\mathfrak{g}$, which we call magical. Such an $\mathfrak{sl}_2$-triple canonically defines a real form and various decompositions of $\mathfrak{g}$.…

We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories,…

In the present paper we study abelian extensions of connected Lie groups $G$ modeled on locally convex spaces by smooth $G$-modules $A$. We parametrize the extension classes by a suitable cohomology group $H^2_s(G,A)$ defined by locally…

We construct an analogue of the classical theta-function on an Abelian variety for closed 4-dimensional symplectic manifolds which are T^2-bundles over T^2 with the zero Euler class. We use our theta-functions for a canonical symplectic…

Let $G = GL_N$ over an algebraically closed field of odd characteristic, and $\theta$ an involutive automorphism on $G$ such that $H = (G^{\theta})^0$ is isomorphic to $SO_N$. Then $G^{\iota\theta} = \{ g \in G \mid \theta(g) = g^{-1} \}$…

Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie…

Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$ on ${\mathbb{P}}^2$, is a very difficult…

We construct an isomorphism between the (universal) spherical Hall algebra of a smooth projective curve of genus g and a convolution algebra in the (equivariant) K-theory of the genus g commuting varieties C_{{gl}_r}={(x_i, y_i) \in…

In this paper we investigate generalized theta divisors $\Theta_r$ in the moduli spaces $\mathcal{U}_C(r,r)$ of semistable vector bundles on a curve $C$ of genus $2$. We provide a desingularization $\Phi$ of $\Theta_r$ in terms of a…

It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We study relations among the classical thetanulls of cyclic curves, namely curves $\mathcal X$ (of genus $g(\mathcal X)>1$) with an automorphism $\sigma$ such that $\sigma$ generates a normal subgroup of the group $G$ of automorphisms, and…

We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C' are curves over a finite field K, with K-rational base points P and P', and…