Related papers: Strange duality for Verlinde spaces of exceptional…

We prove that the pull back of the canonical theta divisor for E_8-bundles at level one induces a strange duality between Verlinde spaces for G_2 and F_4 at level one on smooth curves of genus g. We also prove a parabolic generalization in…

Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P^8 and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual…

The main result of the present paper is the proof of the Strange Duality for elliptic surfaces -- a duality between global sections of determinantal line bundles on moduli spaces of stable sheaves on a fixed elliptic surface. For this, we…

We show that the Verlinde formula for moduli spaces of spin bundles on an algebraic curve gives dimensions of direct sums of spaces of theta functions over the finite set of Prym varieties of unramified double covers of the curve. We then…

For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that the space of sections of certain theta bundle on moduli of bundles of rank r and level k is naturally dual to a similar space of sections of…

We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We show the conjecture is true for the pair ($W(2,0,2),~M(d,0)$) with $d>0$, where $W(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and…

For a compact Riemann surface X of positive genus, the space of sections of certain theta bundle on moduli of bundles of rank r and level k admits a natural map to (the dual of) a similar space of sections of rank k and level r (the strange…

We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial first Chern class and second Chern class 2, and the moduli space of 1-dimensional sheaves…

We examine a sequence of examples of pairs of moduli spaces of sheaves on $\mathbb P^2$ where Le Potier's strange duality is expected to hold. One of the moduli spaces in these pairs is the Hilbert scheme of two points. We compute the…

We determine the splitting type of the Verlinde vector bundles in higher genus in terms of simple semihomogeneous factors. In agreement with strange duality, the simple factors are interchanged by the Fourier-Mukai transform, and their…

We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We focus on the strange duality map $SD_{c_n^r,d}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the…

In this paper, we show a strange duality isomorphism at level one for the space of generalized theta functions on the moduli spaces of alternating anti-invariant vector bundles in the ramified case. These anti-invariant vector bundles…

This paper aims to derive new anomaly cancellation formulas by combining modular forms with E8 and E8*E8 bundles. To this end, we systematically twist and generalize known SL(2,Z) modular forms to define new modular forms associated with…

Let $\mhu$ be the moduli space of semi-stable pure sheaves of class $u$ on a smooth complex projective surface $X$. We specify $u=(0,L,\chi(u)=0),$ i.e. sheaves in $u$ are of dimension $1$. There is a natural morphism $\pi$ from the moduli…

We study Le Potier's strange duality conjecture on a rational surface. We focus on the strange duality map $SD_{c_n^r,L}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the…

In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to sl_5 of the Verma module…

We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering…

Exceptional groups of type $E_6$ contain dual pairs where one member is $\mathrm{Spin}(8)$, and the other is $T\rtimes \mathbb Z/2\mathbb Z$, where $T$ is a two-dimensional torus and the non-trivial element in $\mathbb Z/2\mathbb Z$ acts on…

In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves…

Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a…