相关论文: A characterization of the quantum cohomology ring …

We establish an unfolding theorem for equivariant F-bundles (a variant of Frobenius manifolds), generalizing Hertling-Manin's universal unfolding of meromorphic connections. As an application, we obtain the mirror symmetry theorem for the…

Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold is stably parallelizable then it is shown that the compact…

We develop an approach to calculating the cup and cap products on Hochschild cohomology and homology of curved algebras associated with polynomials and their finite abelian symmetry groups. For polynomials with isolated critical points, the…

We construct a family of fermionic star products generalising the fermionic Moyal product. The parameter space contains the polarisations necessary to define a quantum Hilbert space. We find a star product of fermionic functions on sections…

Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\omega)$. Under some assumptions on $(M,\omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes…

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman…

For a compact monotone symplectic manifold $X$ with Hamiltonian action of a compact Lie group $G$ and smooth symplectic reduction, we relate its gauged $2$-dimensional $A$-model to the $A$-model of $X/\!/G$. This (long conjectured) result…

Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevich's formula has been reinterpreted physically as quantum correlation functions of a topological…

The quantum cohomology ring of the Grassmannian is determined by the quantum Pieri rule for multiplying by Schubert classes indexed by row or column-shaped partitions. We provide a direct equivariant generalization of Postnikov's quantum…

We prove the additive version of the conjecture proposed by Ginzburg and Kaledin. This conjecture states that if X/G is an orbifold modeled on a quotient of a smooth affine symplectic variety X (over C) by a finite group G\subset Aut(X) and…

In the case of an almost simple algebraic group $G$ of type $G_2$ over a field of characteristic $p>0$ we study the cohomology modules of line bundles on the flag variety for $G$. Our main result is a complete determination of the vanishing…

Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH^*(LG) and show that its multiplicative structure…

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…

We consider the Belkale-Kumar cup product $\odot_t$ on $H^*(G/P)$ for a generalized flag variety $G/P$ with parameter $t \in \C^m$, where $m=\dim(H^2(G/P))$. For each $t\in \C^m$, we define an associated parabolic subgroup $P_K \supset P$.…

Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. Essential deformations are classified by the Harrison component of Hochschild cohomology, that vanishes on smooth manifolds and…

For a semisimple adjoint algebraic group $G$ and a Borel subgroup $B$, consider the double classes $BwB$ in $G$ and their closures in the canonical compactification of $G$: we call these closures large Schubert varieties. We show that these…

If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a natural bimodule morphism on the module of sections of the…

Let $G_q$ be the $q$-deformation of a simply connected simple compact Lie group $G$ of type $A$, $C$ or $D$ and $\mathcal{O}_q(G)$ be the algebra of regular functions on $G_q$. In this article, we prove that the Gelfand-Kirillov dimension…

Let $G$ denote a complex semisimple linear algebraic group, $P$ a parabolic subgroup of $G$ and $\mathcal{P}=G/P$. We identify the quantum multiplication by divisors in $T^*\mathcal{P}$ in terms of stable basis, which is introduced by…

We give a positive answer to the Berry-Robbins problem for any compact Lie group G, i.e. we show the existence of a smooth W-equivariant map from the space of regular triples in a Cartan subalgebra to the flag manifold G/T. This map is…