Related papers: Schur Q-functions and a Kontsevich-Witten genus
We describe Zhu recursion for a vertex operator algebra (VOA) on a general genus Riemann surface in the Schottky uniformization where $n$-point correlation functions are written as linear combinations of $(n-1)$-point functions with…
The main goal of this paper is to prove the following two conjectures for genus up to two: 1. Witten's conjecture on the relations between higher spin curves and Gelfand--Dickey hierarchy. 2. Virasoro conjecture for target manifolds with…
For a simple, self-dual, strong CFT-type vertex operator algebra (VOA) of central charge $c$, we describe the Virasoro $n$-point correlation function on a genus $g$ marked Riemann surface in the Schottky uniformisation. We show that this…
We study the representation theory of the Ding-Iohara algebra $\calU$ to find $q$-analogues of the Alday-Gaiotto-Tachikawa (AGT) relations. We introduce the endomorphism $T(u,v)$ of the Ding-Iohara algebra, having two parameters $u$ and…
Eguchi-Hori-Xiong and S. Katz proposed a conjecture that the partition function of topological sigma model coupled to gravity is annihilated by infinitely many differential operators which form half branch of the Virasoro algebra. In this…
We construct the chiral algebra associated with the $A_{1}$-type class $\mathcal{S}$ theory for genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we…
For $q$ generic, Jimbo showed that $q$-tensor space $V_q^{\otimes r}$ (where $V_q$ is the $n$-dimensional vector representation) satisfies Schur--Weyl duality with respect to the commuting actions of the quantized enveloping algebra…
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology…
It is typical for a semi-infinite cohomology complex associated with a graded Lie algebra to occur as a vertex operator (or chiral) superalgebra where all the standard operators of cohomology theory, in particular the differential, are…
We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an…
We generalize the geometric structures generated by Witten's ground ring. It is shown that these generalized structures involve in a natural way some geometric constructions from Self-dual gravity [1,12]. The formal twistor construction on…
This article presents a formula for products of Schubert classes in the quantum cohomology ring of the Grassmannian. We introduce a generalization of Schur symmetric polynomials for shapes that are naturally embedded in a torus. Then we…
The space of local operators in the $Q$-cohomology of the holomorphic-topological supercharge in a four-dimensional $\mathcal{N}=2$ theory carries the structure of a Poisson vertex algebra. This note studies the Poisson vertex algebra…
We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and…
In an odd-dimensional spacetime, gravity can be formulated as a proper gauge theory based on the Chern-Simons action for a suitable gauge group. Performing dimensional reduction, one obtains, as an effective theory, Chamseddine's…
We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth. Such…
The derivation algebras, automorphism groups and second cohomology groups of the generalized loop Schr\"{o}dinger-Virasoro algebras are completely determined in this paper.
The coset $G$-space of a finite group and a subgroup is a fundamental module of study of Schur and others around 1930; for example, its endomorphism algebra is a Hecke algebra of double cosets. We study and review its generalization $Q$ to…
In a previous paper, we proposed a construction of $U_q(sl(2))$ quantum group symmetry generators for 2d gravity, where we took the chiral vertex operators of the theory to be the quantum group covariant ones established in earlier works.…
The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand is given by a product of complex powers of theta functions. We study the structure of the twisted homology and cohomology…