Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAbelianisation of Logarithmic $mathfrak{sl}_2$-Connections
94
0
0.0
(
0
)
Authors
Nikita Nikolaev
Ask ChatGPT about the research
No Arabic abstract
We prove a functorial correspondence between a category of logarithmic $mathfrak{sl}_2$-connections on a curve $X$ with fixed generic residues and a category of abelian logarithmic connections on an appropriate spectral double cover $pi : Sigma to X$. The proof is by constructing a pair of inverse functors $pi^{text{ab}}, pi_{text{ab}}$, and the key is the construction of a certain canonical cocycle valued in the automorphisms of the direct image functor $pi_ast$.
rate research
Read More
We use analogues of Enrights and Arkhipovs functors to determine the quiver and relations for a category of $mathfrak{sl}_2 ltimes L(4)$-modules which are locally finite (and with finite multiplicities) over $mathfrak{sl}_2$. We also outline serious obstacles to extend our result to $mathfrak{sl}_2 ltimes L(k)$, for $k>4$.
Let $X$ be a complex analytic manifold, $Dsubset X$ a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), $j: U=X-D to X$ the corresponding open inclusion, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $U$. In this paper we prove that the canonical morphisms between the logarithmic de Rham complex of $E(kD)$ and $R j_* L$ (resp. the logarithmic de Rham complex of $E(-kD)$ and $j_!L$) are isomorphisms in the derived category of sheaves of complex vector spaces for $kgg 0$ (locally on $X$)
In this paper we study an approximation of tensor product of irreducible integrable $hat{mathfrak{sl}_2}$ representations by infinite fusion products. This gives an approximation of the corresponding coset theories. As an application we represent characters of spaces of these theories as limits of certain restricted Kostka polynomials. This leads to the bosonic (which is known) and fermionic (which is new) formulas for the $hat{mathfrak{sl}_2}$ branching functions.
We discuss the quantization of the $widehat{mathfrak{sl}}_2$ coset vertex operator algebra $mathcal{W}D(2,1;alpha)$ using the bosonization technique. We show that after quantization there exist three families of commuting integrals of motion coming from three copies of the quantum toroidal algebra associated to ${mathfrak{gl}}_2$.
We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
