Related papers: $q$-Hypergeometric solutions of quantum differenti…

In this paper we present a Calder\'{o}n-Zygmund approach for a large class of parabolic equations with pseudo-differential operators $\mathcal{A}(t)$ of arbitrary order $\gamma\in(0,\infty)$. It is assumed that $\cA(t)$ is merely measurable…

We establish a maximal parabolic version of the Kazhdan-Lusztig conjecture \cite[Conjecture 5.10]{CKW} for the BGG category $\mathcal{O}_{k,\zeta}$ of $\mathfrak{q}(n)$-modules of "$\pm \zeta$-weights", where $k\leq n$ and…

If $f$ is an idempotent in a ring $\Lambda$, then we find sufficient \linebreak conditions which imply that the cohomology rings $\oplus_{n\ge 0}Ext^n_{\Lambda}(\Lambda/{\br},\Lambda/{\br})$ and \linebreak $\oplus_{n\ge 0}Ext^n_{f\Lambda…

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…

Let $\Gamma$ be a torsion-free arithmetic group acting on its associated global symmetric space $X$. Assume that $X$ is of non-compact type and let $\Gamma$ act on the geodesic boundary $\partial X$ of $X$. Via general constructions in…

We determine a fundamental solution for the differential operator (Delta - lambda_z)^n on the Riemannian symmetric space G/K, where G is any complex semi-simple Lie group, and K is a maximal compact subgroup. We develop a global zonal…

We consider tautological bundles and their exterior and symmetric powers on the Quot scheme over the projective line. We prove and conjecture several statements regarding the vanishing of their higher cohomology, and we describe their…

The Coleman-Mandula (CM) theorem states that the Poincar\'e and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field…

The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition…

We introduce a new family of symmetric polynomials $\mathfrak{G}^{(\mathbf{u},\mathbf{v})}_{\lambda}$ arising from exactly solvable lattice models associated with the quantised loop algebra $\mathcal{U}_{q}(\mathfrak{sl}_{2}[z^\pm])$. The…

We investigate the analogue of the Quantum Unique Ergodicity (QUE) conjecture for half-integral weight automorphic forms. Assuming the Generalized Riemann Hypothesis (GRH) we establish QUE for both half-integral weight holomorphic Hecke…

Given a holomorphic vector bundle $E:EX X$ over a compact K\"ahler manifold, one introduces twisted GW-invariants of $X$ replacing virtual fundamental cycles of moduli spaces of stable maps $f: \Sigma \to X$ by their cap-product with a…

We give a complete description of the equivariant quantum cohomology ring of any smooth hypertoric variety, and find a mirror formula for the quantum differential equation.

The existence of self-similar solutions is discussed in symmetric teleparallel $f(Q)$-theory for a Friedmann-Lema\^itre-Robertson-Walker background geometry with zero and non-zero spatial curvature. For the four distinct families of…

A one-parameter generalisation R_{\lambda}(X;b) of the symmetric Macdonald polynomials and interpolations Macdonald polynomials is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry,…

The quantum double Schubert polynomials studied by Kirillov and Maeno, and by Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim's presentation of the equivariant quantum cohomology of the flag variety. We define…

We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a class of graphs, which reveals to be a useful tool for…

Let $\Gamma$ denote a finite, undirected, connected graph, with vertex set $X$. Fix a vertex $x \in X$. Associated with $x$ is a certain subalgebra $T=T(x)$ of ${\rm Mat}_X(\mathbb C)$, called the subconstituent algebra. The algebra $T$ is…

The tt*-equation (topological-anti-topological fusion equation) was introduced by S. Cecotti and C. Vafa for describing massive deformation of supersymmetric conformal field theories. B. Dubrovin formulated the tt*-equation as a flat…

This is a paper in a series to study quantum vertex algebras and their relations with various quantum algebras. In this paper, we introduce a notion of T-type quantum vertex algebra and a notion of $G$-covariant $\phi$-coordinated quasi…