Related papers: Quantum ring of singularity $X^{p}+XY^{q}$

Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in the FRT formalism by R-matrices which are…

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show…

In this paper, motivated by Chen--Ruan's stringy orbifold theory on almost complex orbifolds, we construct a new cohomology ring $\mathscr H^\ast_{G,cs}(X)$ for an equivariant almost complex pair $(X,G)$, where $X$ is a compact connected…

Let W be a finite irreducible Coxeter group and let X_W be the classifying space for G_W, the associated Artin group. If A is a commutative unitary ring, we consider the two local systems L_q and L_q' over X_W, respectively over the modules…

We study a quasisymmetric version of the classical Koebe uniformization theorem in the context of Ahlfors regular metric surfaces. In particular, we prove that an Ahlfors 2-regular metric surface X homeomorphic to a finitely connected…

The equivariant quantum $K$-theory ring of a flag variety is a Frobenius algebra equipped with a perfect pairing called the quantum $K$-metric. It is known that in the classical $K$-theory ring for a given flag variety the ideal sheaf basis…

In this paper we develop the definition of a global orthogonal spectrum and its unitary version. It relates $G-$equivariant spectra by equivariant weak equivalence in a coherent way. This category of global spectra has a model structure…

We consider the question whether a Sylow like theorem is valid in the normalized units of integral group rings of finite groups. After a short survey on the known results we show that this is the case for integral group rings of Frobenius…

Wan conjectures that if $X$ and $Y$ form a strong mirror pair of Calabi-Yau varieties over a finite field $F_q$ with $q$ elements, then X and Y have the same number of $F_{q^k}$-rational points modulo $q^k$. We prove this conjecture under…

We compute the structure of the cohomology ring for the quantized enveloping algebra (quantum group) $U_q$ associated to a finite-dimensional simple complex Lie algebra $\mathfrak{g}$. We show that the cohomology ring is generated as an…

We define a Frobenius algebra over fusion categories of the form Rep$(G)\boxtimes$Rep$(G)$ which generalizes the diagonal subgroup of $G\times G$. This allows us to extend field theoretical constructions which depend on the existence of a…

A simple elliptic singularity of type $E_N^{(1,1)}$ ($N=6,7,8$) can be described in terms of a marginal deformation of an invertible polynomial $W$. In the papers \cite{KS} and \cite{MR} the authors proved a mirror symmetry statement for…

It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $ M_{ q,p}(2) $ ( the coordinate ring of $ GL_{q,p}(2) $) exist only when both q and p are roots of unity. In this case th e space of states…

By introducing a result that guarantees a given bialgebra to be a Hopf algebra under a natural condition, we show that the quantum automorphism group of the algebra k[x] of polynomials over a field k (of any characteristic) is the universal…

We give a new proof that for a finite group G, the category of rational G-equivariant spectra is Quillen equivalent to the product of the model categories of chain complexes of modules over the rational group ring of the Weyl group of H in…

We prove a $p$-converse theorem for elliptic curves $E/\mathbb{Q}$ with complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$ in which $p$ is ramified. Namely, letting $r_p =…

We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is…

Let $RG$ denote the group ring of the torsion group $G$ over a commutative ring $R$ with identity. In this paper we present proofs of some statements that appear without to be proved in the literature. We establish the valid implications…

We gave a classification of P and Q with a finite number of K-orbits of a double flag variety G/P*K/Q for a symmetric pair (G, K) when G=GL_{m+n} and K=GL_{m}*GL_{n}, and a description of K-orbits when the number of K-orbits of G/P*K/Q is…

We apply the abelianization technique to obtain an explicit ring presentation for the quasimap quantum cohomology of GIT quotients. As an application, for quiver varieties associated with oriented-acyclic quivers, we establish a cluster…